In a small bowl, combine the chopped pecans, firmly packed light brown sugar, and ground cinnamon. Mix well and set aside for later use.
Preheat your oven to 350°F (175°C). Grease a 9-inch round or 8-inch square baking pan with butter or nonstick spray to prevent sticking.
Place the unsalted butter in a medium saucepan or skillet over medium heat. Cook until the butter melts, begins to foam, and brown specks form at the bottom, releasing a nutty aroma. Remove from heat and let cool to room temperature. You can strain out the browned bits if you prefer a smoother texture, but I like to leave some in for extra flavor.
In a separate bowl, whisk together the all-purpose flour, baking powder, salt, and baking soda until well combined. Set aside.
Using an electric mixer on medium speed, beat the cooled brown butter (from Step 3) and granulated sugar together until thoroughly combined. Add the large egg and vanilla extract, mixing until smooth. Gradually add the flour mixture (from Step 4), mixing just until combined. Stir in the sour cream for added moisture and richness.
Spread half of the cake batter into the prepared pan (from Step 2) and even out the surface. Sprinkle half of the pecan filling (from Step 1) evenly over the batter. Carefully spread the remaining batter on top, then finish by sprinkling the rest of the pecan filling on top.
Bake the assembled coffee cake at 350°F for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Let the cake cool completely in the pan before serving. I always find that letting it cool gives you a cleaner slice and blends the flavors beautifully.