Preheat oven to 325 degrees F (165 degrees C).

Grease a fluted tube pan (such as Bundt®) with 2 tablespoons butter. Add 1/4 cup sugar; shake pan gently until sides are evenly coated with sugar.

Combine remaining 2/3 cup butter and 1 3/4 cup sugar in a large bowl; beat with an electric mixer until light and fluffy. Add eggs one at a time, beating well after each addition. Mix in vanilla extract.

Mix flour, baking powder, and salt together in a bowl. Beat flour mixture into the butter mixture alternately with sour cream, beginning and ending with flour mixture and beating batter well after each addition.

Mix brown sugar and cinnamon together in a small bowl.

Pour 1/3 of the batter into the prepared pan. Sprinkle 1/2 of the brown sugar-cinnamon mixture over the batter. Repeat once more. Pour remaining batter on top. Swirl batter with a butter knife.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour. Cool in the pan for 5 minutes; invert onto a wire rack to cool completely.