Beat together the butter, sugars, molasses, salt, and pumpkin pie spice until light and creamy., Beat in the egg, pumpkin purée, pumpkin flavor, and vanilla., Stir in the flour in three additions, mixing until the dough comes together., Divide the dough in half, shape both halves into disks, wrap in plastic, and refrigerate for at least 1 hour., Preheat the oven to 300°F. Grease two baking sheets, or line them with parchment., Working with one piece at a time, flour your work surface and roll the dough 1/4" thick., To shape cookies using a Springerle mold: Brush a very light coating of flour onto the dough and your Springerle mold. Press the mold firmly into the dough, then remove and cut around the design with a knife or a fluted pastry wheel., To shape cookies using a Springerle pin: Use a regular rolling pin to roll each disk of dough into a 1/4"-thick rectangle, roughly the same width as your Springerle pin. Use a pastry brush to brush a very light coating of flour onto the dough. Flour your Springerle pin, then give it a couple of sharp raps to knock off any excess. Slowly roll the Springerle pin over the dough, pressing down hard enough to leave a good impression. Cut the cookies apart on the lines, using a pastry wheel or knife., Transfer the cookies to the prepared baking sheets., Freeze the cookies for at least 30 minutes; this helps them retain their shape during baking., Bake the cookies for 30 minutes, until they're firm and dry looking; rotate the baking sheets halfway through. Remove the Springerle from the oven, and cool completely right on the pan., To make the glaze: Combine all the ingredients, stirring until smooth. Add enough milk to make a thin, pourable glaze., Dip the unstamped side of each cookie into the glaze; set the Springerle on a rack, and let the glaze set until firm.