Preheat oven to 425°F (220°C). Put butter in a 9x13-inch baking dish and place the dish in the oven until butter is melted.

Mix baking mix, lemon-lime soda, and sour cream together in a bowl until dough holds together and is sticky. Turn dough onto a floured work surface and roll into a 1-inch thick circle. Cut circles out of the dough using a cookie cutter or the rim of a wine glass.

Place dough circles in the melted butter. Bake in the preheated oven until biscuits are golden brown, 10 to 12 minutes.