Mix baking mix, milk, egg, 2 tablespoons sugar, and cinnamon together in a bowl with a whisk, beating vigorously for 20 strokes. Transfer dough to a floured work surface and knead 5 times. Roll dough into 1/2-inch thickness and cut with a floured doughnut cutter. Place doughnuts onto a baking sheet.
Bake in the preheated oven until cooked through and lightly browned, 7 to 9 minutes.
Pour melted butter into a bowl. Place 1/2 cup sugar in a separate bowl. Dip doughnuts into butter; transfer to sugar and lightly press until doughnuts are coated.