Preheat oven to 375°F. Line 2 baking sheets with parchment.
Make dough: Whisk together first 7 ingredients. In a separate bowl, cream butter and brown sugar until pale; beat in eggs. Mix in pumpkin, evaporated milk and vanilla, followed by flour mixture gradually.
Put some dough in a large plastic bag; snip a corner. Pipe 2 1/2-inch rounds about 1/2-inch thick onto sheets. Continue with rest of dough. Bake, rotating halfway through, until tops spring back when touched, about 12 minutes. Top each with a half marshmallow; bake for 1 1/2 minutes. Transfer, on parchment, to racks; cool.
Make icing: Using an electric mixer, beat cream cheese and butter until smooth. Add confectioners' sugar a little at a time until icing is thick but spreadable. Add food coloring.
Gently frost cookies over marshmallow. Let set for 20 minutes. Pipe icing faces and stems onto each cookie.