I'm going to speak specifically about Henry VIII, as it's him and his court who I am most familiar with on this particular topic, and because I personally think it's the perfect example of the height of Tudor opulence.

Henry's own personal favorite foods included:

venison, game pies stuffed with oranges, haggis, eels, baked lampreys, salmon, sturgeon, ling, and an early version of beef olives (beef stuffed with forcemeat and vegetables). For the void, he preferred custards, fritters, tarts, jelly and cream of almonds. (1)

Court meals would have been several courses with multiple dishes. The diet would have been quite meat heavy, even considering that no meat was to be eaten on a Friday, only fish. Luckily for the Tudors, "fish" included eel, crab, whale, most poultry (chicken, swan, peacock dressed in its own feathers), porpoise, and seal. (2)

The royal court’s annual provision of meat consisted of:

• 1,240 oxen

• 8,200 sheep

• 2,330 deer

• 760 calves

• 1,870 pigs

• 53 wild boar (3)

And:

And if they [the nobles and many of their servants] do not have 20 varied meat dishes at dinner and supper, they consider themselves slighted.’

(‘A dialogue between Cardinal Pole and Thomas Lupset, Lecturer in Rhetoric at Oxford’, 1529-32)(3)

Spices were very popular, and an indicator of ones wealth as they were very expensive at this time, so you can imagine a lavish court like Henry's would have a truly abundant amount of spices. Henry had a special staff of servants responsible for his spicery. He also had servants of the pantry, cellar, lardar, scullery (dishwashers), and woodyard, overseen and managed by clerks and underclerks of the kitchen - a truly enormous staff was needed to take care of the king and his court. (2)

As to how things tasted, well, here's a few recipes:

Chykonys in bruette. — Take an Sethe Chykonys, & smyte hem to gobettys ; þan take Pepir, Gyngere, an Brede y-grounde, & temper it vppe wyth þe self brothe, an with Ale ; an coloure it with Safrouw, an sethe an serue forth. (4)

More or less translates to:

Chickens in broth - take and seethe chickens, and smite them to gobbets, then take pepper, ginger, and bread ground, and temper it with the same broth, and with ale, and color it with saffron, and seethe and serve forth.

Or

Sauce for shulder of moton.— Take percely, and oynons, and mynce þem and þe rostyde shulder of Moton; and take vynegre, and poudre gingre, salt and cas a-pon þe mynced shulder, and ete hym so. (4)

Again, translation is more or less:

Sauce for a shoulder of mutton - take parsley, and onions, and mince them and the roast shoulder of mutton, and take vinegar, and powdered ginger, salt and cast upon the mince shoulder, and eat him so.

Other recipes use mace, almonds, garlic, wine sauces, and cloves. They might not be your mom's meatloaf, but probably would be mostly edible to modern diners. Though we would probably take a pass on the lamprey.

Sources:

1. Henry VIII: The King and His Court - Allison Weir

2. A collection of ordinances and regulations for the government of the royal household, made in divers reigns : from King Edward III to King William and Queen Mary, also receipts in ancient cookery - Society of Antiquaries of London

3. A History of Royal Food and Feasting - University of Reading via futurelearn.com

4. Two fifteenth-century cookery-books - Thomas Austin

Follow up questions: how did the average commoner's kitchen or food preparation area look in comparison to the royal/noble's kitchen?

My understanding for many castles is that kitchens were often separated from the main house/keep as a fire precaution. Did the common person have any way to take precautions like that or did they just do their best not to burn their house down?