Place olive oil, balsamic vinegar, garlic, brown sugar, thyme, dry mustard, and paprika into a food processor; blend until combined. Pour marinade into a resealable plastic bag. Add pork tenderloin to the bag, seal, and marinate in the refrigerator for 24 hours.

Preheat the oven to 250 degrees F (120 degrees C).

Transfer pork with marinade to a Dutch oven.

Bake in the preheated oven for 3 hours.

Transfer pork from the Dutch oven to a plate, reserving drippings in the pan. Cover pork to keep warm and set aside.

Heat drippings in the Dutch oven over medium heat on the stovetop. Pour in sherry and bring to a boil while scraping the browned bits of food off the bottom of the pot with a wooden spoon.

Stir together cornstarch and water in a small bowl; add to sauce in the pot. Bring to a simmer and cook until thickened, about 15 minutes.