You should take a look at proponents of global history, like Sanjay Subrahmanyam (well, since his first steps in India, he has also been teaching in Paris, Oxford and the US, but that's what happens to virtually every gifted and visible researcher from non-western countries). His main interest is Indian history, which has led him to write many things on the history of Portugal (notably a fine biography of Vasco da Gama), and I know that he has an ongoing research project on an old question — how to explain the unexpected take-off of Europe in terms of economic and political power during the modern era?

There are certainly other occasional examples.

I think a lot of this kind of work gets done by non-Western academics writing about the postcolony. In turn, they reflect upon the metropole (Europe) in the context of how its imperial ventures serve particular needs, or how a specific metropolitan population convinced itself to undertake and then to continue an imperial venture.

If that sounds interesting to you, I'd point you to V.Y. Mudimbe, Achille Mbembe, Mahmood Mamdani, Edward Said, Kwame Appiah, and Oyeronke Oyewumi.

For the middle ages, look to Arab and Muslim sources (though they are often one and the same at this time). Here's a brief selection below:

(1) Ibn Khaldun -- lots of stuff, arguably one of the most important Muslim writer of the middle ages.

(2) Ibn Shaddad. The Rare and Excellent History of Saladin

(3) The Story of Bayad and Riyad - though not explicitly about Europe it is important that it survived in Spain for so long when many other muslim sources did not.

(4) Ioannes Scylitzes.

(5) Ibn Battuta - along with Ibn Khaldun, one of the most important medieval muslim writers.

(6) al-Umari

Secondary Sources:

(1) James Muldoon. Travellers, intellectuals, and the world beyond Medieval Europe (2010)

(2) Maria Rosa Menocal. The ornament of the world : how Muslims, Jews, and Christians created a culture of tolerance in medieval Spain (2002).

(3) Paul Kunitzsch. The Arabs and the stars : texts and traditions on the fixed stars, and their influence in medieval Europe (1989).

(4) Emran Qureshi; Michael Anthony Sells. The new crusades : constructing the Muslim enemy (2003)

(5) Minou Reeves; P J Stewart. Muhammad in Europe (2000)

(6) Remi Brague. The legend of the Middle Ages : philosophical explorations of medieval Christianity, Judaism, and Islam (2009).

Hope this helps a little. Happy Reading!