Place the dry ingredients in a bowl and gently stir with a whisk. Set aside.
In the bowl of a standing mixer fitted with a flat beater, or in a large bowl with an electric hand mixer, place the butter and confectioner’s sugar. Blend well until fluffy.
Blend in the egg and extracts.
Gradually blend in the flour mixture.
Cover and refrigerate the dough for two hours.
Preheat oven to 375 degrees F.
On a lightly floured surface, roll out the cookie dough to 3/8-inch thickness. Cut out your desired shapes and place on a baking tray lined with parchment paper.
Gently insert lollipop sticks into the bottom of the cookies. Make sure the stick is securely in the cookie and that the sticks do not touch each other or other cookies. Keep any dough or trays of cookies in the refrigerator while other cookies bake.
Bake for 17 to 22 minutes, or until cookies are firm in the center. Cookies of a different size or thickness may need less or more cooking time.
Let the cookies cool and frost.
For the Frosting:
In the bowl of a standing mixer fitted with a wire whip, or in a large bowl with an electric hand mixer, place the butter, confectioner’s sugar, 3 tablespoons of milk, the extracts and salt. Beat on low until the ingredients are mixed, then increase speed to medium until the frosting is well blended.
Add additional milk until desired consistency is reached.
If preferred, divide and tint the frosting with food coloring. Prepare decorating bags with decorating tips, fill with frosting and pipe to decorate the cookies.