Melt the butter in a small saucepan over medium heat, whisking constantly. Continue cooking until it turns golden brown and gives off a nutty aroma, about 4 to 5 minutes. Pour into a heat-safe bowl and cool completely.
Preheat the oven to 425°F. Line a standard 12-cup muffin pan with paper liners or lightly coat with nonstick spray.
In a large mixing bowl, whisk together the cooled butter and brown sugar until smooth and combined.
Add the eggs one at a time, whisking after each. Stir in the vanilla, pumpkin puree, milk, cinnamon, and pumpkin spice until fully combined.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Mixing these separately ensures the leavening is evenly distributed.
Gently fold the dry ingredients into the wet mixture using a spatula. Mix just until combined - overmixing can make muffins tough.
Fold in the dark chocolate chips, reserving a handful for topping. Let the batter rest for 15 minutes on the counter. This rest period helps the muffins rise higher.
Divide the batter evenly among the muffin cups, filling each about three-quarters full. Sprinkle the reserved chocolate chips on top for a bakery-style finish.
Place the pan in the oven and bake at 425°F for 5 minutes. Then, reduce the oven temperature to 350°F (without opening the oven) and bake for 17 to 20 more minutes. The muffins are done when a toothpick inserted in the center comes out clean.
Allow the muffins to cool in the pan for 5 minutes, then transfer them to a wire rack. Enjoy!