1. Prepare the Cookie Dough:

1. In a large bowl, beat the softened butter and sugar together until light and fluffy.
2. Add the egg, vanilla extract, and peppermint extract. Mix until combined.
3. In a separate bowl, whisk together the flour, baking powder, and salt. Gradually mix the dry ingredients into the wet mixture until a soft dough forms.
4. Divide the dough in half. Tint one half with red gel food coloring and knead until evenly colored.

2. Form the Striped Dough:

1. Roll out both the red and plain doughs into equal-sized rectangles, about 1/4-inch thick.
2. Place the red dough on top of the plain dough. Gently roll them together with a rolling pin to adhere the layers.
3. Cut the dough into thin strips (about 1/2-inch wide). Stack the strips alternately, flipping every other strip to create a striped effect. Gently press the strips together.
4. Chill the dough for 30 minutes.

3. Bake the Cookies:

1. Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper.
2. Slice the chilled dough into 1/4-inch thick rounds. Place the slices on the prepared baking sheets, spacing them 2 inches apart.
3. Bake for 8-10 minutes, or until the edges are set. Cool completely on a wire rack.

4. Make the Peppermint Filling:

1. In a bowl, beat the butter until creamy. Gradually add the powdered sugar and peppermint extract.
2. Add heavy cream, 1 tablespoon at a time, until the filling is smooth and spreadable.

5. Assemble the Cookies:

1. Spread a layer of peppermint filling on the flat side of one cookie. Top with another cookie to create a sandwich.
2. Roll the edges in crushed peppermint candies, if desired.