Preheat the oven to 425°F. Brush the inside of 10-inch round cast iron or other ovenproof skillet with the 2 Tbsp. melted butter.
Place the 2 1/4 cups flour, sugar, baking powder, baking soda, salt and spices into a bowl and whisk to combine. With your fingers, two forks or a pastry cutter, work the 1/4 cup butter into the flour mixture until thoroughly distributed. Gently mix in the milk until a loose dough forms. Flour a work surface, and then turn the fairly wet and sticky dough onto it.
Lightly flour your hands and gently shape the dough into a 18-inch long log. Slice the log, widthwise, into 12 equal pieces. Shape each slice into a ball and set them in circular fashion in the skillet, not or just barely touching. Brush the top of each dough ball lightly with beaten egg. Bake the shortcakes in the middle of the oven 12 to 13 minutes, until puffed. Turn the oven to broil, and broil 1 to 2 minutes, or until the tops of the pumpkin shortcakes are golden brown.
Remove from the oven and let cool on a baking rack while you make the glaze. To do so, place the dulce de leche, coffee and vanilla in a small pot and set over medium heat. Whisk and heat the mixture until hot, smooth and fluid, and then remove from the heat.
Use a small spoon to drizzle the dulce de leche mixture over the pumpkin spice shortcakes. Now sprinkle on the walnuts. Serve the pull-apart shortcakes warm or at room temperature. Top servings, if desired, with a dollop of whipped cream.