Preheat oven to 350 degrees. Line two baking sheets with parchment paper; set aside.
COOKIES: In a medium bowl, whisk together flour and baking powder; set aside.
In a large bowl, using an electric hand mixer, cream butter on medium-high for 1-2 minutes, or until butter is smooth and lighter in color. With the mixer on low, slowly add in the sugar, and then the egg and extracts. Add the flour mixture, a 1/2 cup at a time, until fully incorporated.
Divide cookie dough in half. Place half back in the bowl and the other half in a separate bowl. Add 1 teaspoon red food coloring to one bowl and 1 teaspoon green food coloring to the other bowl. Beat each color until fully incorporated.
Roll out each section of dough on lightly floured surface into rectangle that is slightly thicker than 1/8-inch. Cut rectangles into 3/4-inch strips. Weave the red strips over and under the green strips, creating a basket like appearance. Slightly press down with rolling pin to seal together.
Cut weaved dough using 4-inch mitten-shaped cookie cutter dipped into flour. Using small metal spatula, place onto prepared cookie sheets.
Use remaining dough to create marbled mitten cookies. Gently press dough together. Roll out to 1/8 to 1/4-inch thickness. Cut with mitten-shaped cookie cutter. Place onto prepared cookie sheets.
Bake cookies for 8-10 minutes or until lightly browned. Remove to cooling rack to cool completely. Decorate the bottoms with buttercream frosting.
BUTTERCREAM FROSTING: In a large bowl, beat butter on high speed until the butter has lightened in color and is thoroughly whipped
On low speed, add 1 cup confectioners’ sugar and salt; beat until combined. Add milk and extract; beat until combined.
Add remaining confectioners' sugar; beating until incorporated. Turn mixer to high speed and beat frosting until light and fluffy. Add more milk or cream as needed if the mixture becomes too thick or dry.
Fill a piping bag with frosting fitted with a 1M tip. Pipe the bottom of the mittens with frosting.
Yields 12 basket weave cookies & 12 marbled mitten cookies