The straightforward answer is that we don't know, because we've nothing to test against. The more useful answer is that except with some very specific ingredients, we can be pretty sure that things will not taste the same.

There are two principal reasons for this, and they are as you've surmised: ingredients and preparation.

Let me look at some ingredients first. Take aubergines (eggplants) - they were for most of their history very bitter. In order to cook with them, you had to go through a process of slicing and salting them, to draw out the bitter liquids, and then washing off the salt. This is no longer necessary with the modern aubergine, which has been bred to be much sweeter. So you can use the modern aubergine unsalted, but the taste of the final dish will not have the bitter undertaste that the original had. And if you salt the modern vegetable, it actually loses some of the the taste it does have.

Similarly, brassicas are a bit of a mystery in general. Cabbages, cauliflowers, Brussels sprouts and a few other things are in fact all (more or less) the same plant. You'd need a botanist to tell you if it's one species, or what, but the point is that they develop new varietals very quickly, and revert to less useful states equally quickly, in just a few generations. So what we have as 'cabbage' is almost certainly not what our ancestors had, and they certainly had a few generic green plants we don't.

There have also been improvements - in yield, size of vegetable, and taste - in onions, garlic, carrots, lettuces (previously also quite bitter), radishes, and pretty nearly every commonly used vegetable. And then there are the plants with many varieties, of which apples are probably the best example. If you have one particular kind of apple - Cox's Orange Pippin, say - it may actually be identical to the older form of the same variety, because of the ways in which apples are propagated by grafting, which is essentially a crude form of cloning. Apples don't breed true, though, so if you plant apples rather than graft them, you get a very different fruit. And a number of the varieties we used to have - there were literally hundreds - have been completely lost.

Spices will also have changed, though in many cases not as much - the various plants to produce spices, chili peppers aside, are not as selectively bred, largely due to growing in poorer areas of the world. However, our modern spices, because they arrive much more quickly from the places in which they're grown, tend to be vastly stronger. You could simulate the spices of past times by leaving them in a cupboard in an unheated, uninsulated building for a few years - or you could just use less than the recipe calls for. Vanilla, because it retains flavour pretty strongly, is possibly less affected by this than most.

Obviously, meat animals, and chickens and ducks for eggs, have been bred entirely differently in the last two hundred years. They're bigger, they produce more meat, they're slaughtered at very precise ages rather than having that dictated by seasons and food supply, and so on. And pork, for instance, is very much influenced by the food that the pigs eat, so that the traditional acorn-fed pig of medieval Europe just isn't possible any more.

There is, however, the possibility of foraged food and wild game. Neither has changed a lot since the Middle Ages, although the food that the game eats will have altered in some cases with modern farming. The wild European "Alpine" strawberry is pretty much unchanged, for instance, and that's what was used in any recipe involving strawberries from before the Colombian Exchange. The modern strawberry is a crossbreed between these and a New World fruit. Pigeons and wild ducks are also pretty similar to the way they were.

Then there are the technical aspects, which verge over into the preparation end of things. Milling, for instance, is a much more refined technique now than it was 300 years ago, although the date of 1837 had pretty good milling already. For older recipes, though, where it says "flour", you could expect the original to be a much coarser flour than you'd buy in modern grocery shop.

In other preparation terms, a modern oven or stovetop, with its steady temperatures, makes cookery entirely different. Medieval ovens were heated by a fire burned directly in them, with the coals then raked out, and the baked goods cooked inside the thus-warmed chamber. Even more recent ovens - such as those available in the 1800s - would have been fueled by wood or coal, and thus were variable in heat depending on how recently they'd been fueled. And everything, of course, got more than a tinge of smoke in the taste, which only happens now if you burn something.

So overall, your cookies probably don't taste the same. They would be recognisable from an 1837 recipe, though, since milling hasn't changed that much, and while the spices would be stronger now, they wouldn't be all that different in taste. If you were working from an older recipe - 1600s - then you'd have larger differences to contend with, and when I'm cooking from al-Warraq, a 10th century Baghdadi cookbook, I have to resign myself to the idea that what I'm producing is more in the line of a tribute than a replica.