In a medium-sized mixing bowl, combine the flour, softened butter, and heavy cream. Mix until a soft dough forms. Divide the dough into three equal portions, wrap each in plastic wrap, and refrigerate for at least 1 hour, or until the dough is firm.

Preheat the oven to 375°F (190°C). Line two baking sheets with parchment paper. Set aside.

Remove one portion of dough from the refrigerator. On a lightly floured surface, roll it to approximately 1/8 inch thickness. Keep the remaining dough refrigerated until needed. Cut the dough using 1 1/2-inch cookie cutters into desired shapes.

Place a generous amount of decorating sugar on a sheet of waxed paper. Coat both sides of each cookie cutout in the sugar by pressing lightly into the surface. Transfer cookies to the prepared baking sheet and prick each one with a fork 3–4 times to prevent puffing.

Bake in the preheated oven for 7 to 9 minutes, or until the cookies are set but not browned. Remove from oven and allow them to cool completely on a wire rack—about 1 hour.

In a small bowl, beat together the powdered sugar, softened butter, and chosen extract until smooth and creamy. Add a drop or two of food coloring if desired.

Pair the cooled cookies by size. Pipe or spread a small amount of the filling onto the flat side of one cookie, then gently press another cookie on top to form a sandwich. Repeat with remaining cookies.