Stir 1 tablespoon softened butter and white sugar together in a coffee mug until fluffy; stir egg, sour cream, and vanilla extract into the butter mixture. Add 1/4 cup flour and baking powder into the mixture; stir until smooth.
Mix 2 tablespoons flour, brown sugar, and cinnamon together in a bowl. Mash 1 tablespoon butter into the flour mixture with a fork or pastry cutter until mixture is crumbly; sprinkle over the cake batter in the mug.
Cook in microwave oven on high for 1 minute. Continue cooking in 10-second intervals until a toothpick inserted into the middle comes out clean.