Preheat the oven to 350°F.
Place the butter in a light-colored saucepan and melt over high heat. Once the butter begins to bubble, reduce the heat to medium-low. Stirring every so often to keep the milk solids from burning and sticking to the bottom of the pan, continue to cook the butter until it turns an amber-colored brown and the milk solids have darkened. This will take 5 to 8 minutes. It is done when the brown butter smells nutty and toasty. Pour the brown butter into a heat-safe container. Set aside to cool.
In a large mixing bowl, stir together the flour, both sugars, baking powder, cinnamon and salt. Set aside.
Pour the oil and vanilla into the browned butter and stir to combine.
Make a well in the center of the dry ingredients. Add the butter mixture, eggs, and milk. Whisk until the batter begins to thicken then switch to a rubber spatula. Stir together the batter until combined.
Line 2 muffin tins with 20 cupcake liners. Use a spring-loaded cookie scoop to fill the liners up half way.
Sprinkle a pinch of cookie crumbs (about 2 teaspoons) on each cupcake. Every distribute the rest of the batter. Top the cupcakes with more crumbs.
Bake the cupcakes for 20 to 22 minutes, or until a toothpick inserted into their centers comes out clean or with a few moist crumbs. Allow the cupcakes to cool on a wire rack.
Once cool, use the tip of a knife or an apple corer to remove the centers of the cupcakes. Do not cut all the way through.