These are tender "cakey" cookies. Lift them off pans carefully.
Preheat oven to 350º F. Line cookie sheets with parchment paper or spray with nonstick cooking spray.
In a large mixing bowl, stir together flour, cream of tartar, baking soda, baking powder, salt, and pumpkin-pie spice. Set aside.
Place butter and oil in a mixing bowl. Beat with an electric mixer on low speed until well mixed. Increase speed to medium and continue beating until mixture is light and fluffy, about 3 minutes.
Add brown sugar and beat until smooth. Beat in pumpkin puree, egg, egg yolks, vanilla and lemon extracts. Gradually beat in flour mixture, finishing by hand if the batter becomes too thick for beaters. Stir in oats by hand.
Drop batter (about 2 1/2 tablespoon) into mounds on prepared cookie sheet about 4 inches apart. Make cookies as round as possible,smoothing with the blunt side of a knife. (Each cookie should be about 2 1/2 inches round.)
Place pan in upper third of preheated oven and bake for 6 minutes. Remove pan and press a marshmallow half in center of each cookie, tapping marshmallow gently but firmly down into the dough. Continue baking for 4 minutes, or until edges are slightly darker. Remove pan from oven and cool on a rack for several minutes.
Using a spatula, carefully transfer cookies to wire racks and cool completely. Tap each cookie gently with back of the spatula to deflate the marshmallow.