1 cup unsalted butter, room temperature, divided
1/2 cup granulated sugar
1/2 cup packed light brown sugar
1 large egg
1 tablespoon milk
2 teaspoons vanilla extract, divided
1 cup uncooked quick-cooking oats
3/4 cup all-purpose flour
1/4 cup unsweetened cocoa powder
1/2 teaspoon baking soda
1/4 teaspoon salt
1/2 cup semisweet chocolate morsels
1 and 1/2 cups confectioners' sugar
4 tablespoons pumpkin puree
orange food coloring
Beat 1/2 cup butter along with granulated sugar and brown sugar until light and fluffy. Add egg; beat until blended. Reduce speed to low; add milk and 1 teaspoon vanilla. In a small bowl, combine oats with flour, cocoa powder, baking soda, and salt. Gradually beat into butter mixture just until blended. Stir in chocolate morsels. Cover and chill for 30 minutes.
Preheat oven to 350 degrees. Drop dough evenly in 2 tablespoon mounds onto parchment-lined baking sheets. Bake for 10 minutes. Cool on baking sheets 1 minute then transfer to wire racks to cool.
Beat remaining 1/2 cup butter and confectioners' sugar at medium-high speed with an electric mixer until creamy. Add pumpkin; beat until blended. Add remaining 1 teaspoon vanilla and orange food coloring, as desired; beat well.
Arrange half the cookies upside down on a work surface. Spoon frosting over center of cookies. Top with remaining cookies pressing gently to distribute frosting.