Preheat oven to 350° (325° if using convection heat).
In a bowl, with a mixer on medium speed, beat butter, granulated sugar, and brown sugar until blended, then beat on high speed until creamy. Add eggs and vanilla and beat until well blended. Add flour, baking powder, cinnamon, nutmeg, and salt; beat on low speed until combined, then on medium speed until well blended. Divide dough into three portions.
Place each portion between two sheets of floured plastic wrap. Roll dough evenly into flat rounds about 1/4 inch thick. Stack rounds on a baking sheet and chill until firm, at least 45 minutes, or up to 2 days.
Working with one portion of dough at a time (keep remaining chilled), peel off top sheet of plastic wrap. Set floured pattern (see notes) on dough and cut around edges. Or with floured round cookie cutters (3-in. diameter), cut out cookies, placing cutters as close together as possible. Transfer to cooking parchment-lined or ungreased baking sheets, placing cookies about 1 inch apart. Repeat with remaining dough rounds. Gather up scraps and press together into a ball. If dough is still cold, roll and cut out remaining cookies. If it's soft and sticky, repeat step
Bake cookies until firm to touch and slightly darker brown around edges, 8 or 9 minutes; if baking more than one sheet at a time in one oven, switch positions halfway through baking. Slide parchment with cookies off sheets onto racks or counter to cool, then remove from parchment. Or cool on pans about 1 minute and then transfer to racks to cool completely. If not using cooking parchment, wipe off baking sheets after each batch. Cool sheets before filling with more cookies.
Spread icing over cookies and decorate with candies, using candy corn for a beak and chocolate chips for eyes. Let stand until icing is firm, about 5 minutes.
Icing: In a small bowl, stir together 2 cups powdered sugar and just enough milk (about 3 tablespoons) to make a spreadable icing. If desired, tint with food coloring. If icing thickens as it stands, stir in a few more drops of milk.