Heat an oven to 400°F or prepare charcoal for cooking outdoors by heating coals in a chimney starter until hot and ashy.
Butter the bottom and sides of a 5-quart Dutch oven. If using fresh cherries, rinse, stem and pit the cherries. If using frozen, place the cherries into a colander and allow to thaw completely before using. Discard the juice. Spread the cherries evenly over the bottom of the Dutch oven.
In a large mixing bowl, whisk together the eggs and sugar until frothy and lightened in color. Add the milk, vanilla, and flour and whisk to combine. Pour the batter over the cherries.
To bake in the oven: Bake on the middle rack, uncovered, for 30 minutes or until golden on top and a knife comes out clean when inserted into the middle.
To bake outdoors: Place 18 to 19 coals on a Dutch oven table. Place a cooling rack, or other wire rack, that is at least 2 inches high, directly over the coals. Place the Dutch oven on the rack directly over the coals. Cover with the lid and place 22 to 23 coals on top. Cook with the lid on for 25 minutes. Remove the lid and cook for another 5 minutes or until golden on top and a knife comes out clean when inserted into the middle.
Cool for 30 minutes before removing from the Dutch oven, slicing and serving.