Preheat the oven to 350 degrees F. Butter and flour a pie pan or other round baking dish that measures at least 2” high and 9” wide. Scatter the cherries evenly about the pan.
In a mixing bowl, whisk together the eggs and flour, then add the sugar and baking powder and vanilla and whisk again until combined. Slowly pour in the milk and whisk until the batter is smooth. Pour over the cherries and bake until set and lightly browned, about 40 minutes.