Place an oven rack in the middle position and preheat the oven to 400ºF. Grease a 12 cup muffin pan or line with paper liners.
In a small saucepan, melt the butter over medium heat. Keep an eye on it, stirring frequently, allowing it to cook down until the butter foams, crackles, and begins to brown. Remove from the heat and pour into a small bowl to cool.
In a large bowl, whisk together flour, baking powder, baking soda, spices, and salt. In another large bowl, whisk together eggs and brown sugar until well combined. Add the slightly cooled butter, a little at a time, until creamy. Stir in applesauce. Fold the wet ingredients into the flour mixture until just moistened, then gently fold in the nuts. Divide the batter evenly among the muffin cups and top with raw or coarse sugar and more pecan pieces if desired.
Bake in the preheated oven until puffed and golden, about 20 minutes. Cool in the pan on a rack for 5 minutes, then remove to cool completely. These are best eaten the day they are made.