In a small saucepan, melt the butter over moderate heat. Cook, stirring constantly, until the butter is melted and begins to foam and sizzle and turn a golden brown color, about 3 minutes. The milk solids at the bottom of the pan will be toasty brown and the butter should smell intensely buttery and nutty. Transfer to a medium bowl and let cool slightly. Add the maple syrup, egg, brown sugar, rum, and spices. Whisk until smooth. Stir in the chopped toasted pecans.
Portion the dough into two dozen 1-inch balls—about 1 scant tablespoon each. (It’s optimal to do this before you begin pressing in the dough to make sure it is evenly distributed—a #60 level scoop also helps with portioning.) Press each ball into the well of a nonstick mini-muffin pan, spreading evenly over the bottom and ¾ of the way up the sides (slightly higher if the cups are on the shallow side).
Add a heaping teaspoon of the filling to create a small mound in each cup, making sure to distribute the pecans evenly by stirring the filling every few scoops. Bake the tassies until the filling is set and the crust is golden brown, 20 to 25 minutes. Transfer to a wire rack to cool for 10 minutes, then remove the tassies from the tin to cool completely.