Preheat oven to 375 degrees F. Butter a 9-inch cast-iron pan or 2-quart baking dish and dust with granulated sugar.
Place the eggs, granulated sugar, zest, milk, salt, vanilla seeds, liqueur and basil in a blender. Blend at high speed until the ingredients are combined, about 1 minute. Add the flour and blend at high speed for 1 to 2 minutes. Allow the mixture to rest for 30 minutes at room temperature.
Place the cherries into the buttered pan. Pour the egg mixture over the fruit. Immediately place the pan in the oven. Bake for 30 to 35 minutes or until golden brown and puffy. Insert a toothpick in the center, to test for doneness; it's ready when it comes out clean.
Dust with powdered sugar, cut into wedges and serve.