Preheat oven to 350 degrees F (175 degrees C). Coat the inside of a tube pan with 1 tablespoon melted butter and 1 tablespoon flour.
Combine 2 3/4 cup flour, baking powder, baking soda, and salt in a bowl.
Beat butter and sugar with an electric mixer in a large bowl until light and fluffy. The mixture should be noticeably lighter in color. Add eggs one at a time, allowing each egg to blend into butter mixture before adding the next. Beat vanilla into the mixture with the last egg. Pour flour mixture alternately with the sour cream into the butter mixture, mixing until just incorporated into a batter.
Mix blueberries, brown sugar, walnuts, and cinnamon.
Spread about 1/3 the batter into the bottom of the prepared pan. Sprinkle about 1/3 the blueberry mixture over the batter layer. Spread about 1/2 the remaining batter over the blueberry mixture; top with about 1/3 the remaining blueberry mixture. Spread remaining batter over the blueberry mixture. Top with remaining blueberry mixture.
Bake in the preheated oven until golden and the tops spring back when lightly pressed, 60 to 65 minutes.