Combine the pecans, brown sugar, and cinnamon. Set aside.
To make the cake:
Preheat oven to 350°F (175°C). Grease a 9-inch round or 8-inch square baking pan.
Place the butter in a medium saucepan or skillet. Cook over medium heat until the butter melts and begins to foam.
Continue cooking, stirring occasionally, until brown specks begin to form at the bottom of the pan and the butter has a nutty aroma. Remove the pan from the heat and allow to cool to room temperature. If desired, strain the butter to remove some or all of the browned bits.
Whisk together the flour, baking powder, salt, and baking soda. Set aside.
Using an electric mixer on medium speed*, beat the cooled butter and sugar until thoroughly combined. Add the egg and vanilla, and mix until thoroughly combined.
Gradually add the flour mixture, and mix just until combined. Stir in the sour cream.
Transfer half of the batter to the prepared pan, and spread evenly. Sprinkle half of the filling/topping mixture over the cake batter. Carefully spread the remaining cake batter on top of the filling. Sprinkle the remaining filling/topping on top of the batter.
Bake 30 to 35 minutes, or until a pick inserted into the center comes out clean. Cool completely in the pan before serving.
Notes
*You may also mix this cake by hand if you prefer.