In the bowl of a stand mixer, combine all-purpose flour, good quality unsalted butter, and heavy whipping cream. Mix until the ingredients are just combined into a soft dough. Cover the bowl tightly with plastic wrap and refrigerate the dough for at least 2 hours. This chilling step helps the dough firm up, making it easier to handle later.
Preheat your oven to 375°F (190°C) while you wait for the dough to chill. Prepare a small bowl with granulated sugar and set it aside for later use.
After the dough has chilled, take about one-third of it out of the refrigerator, keeping the remaining dough chilled. On a lightly floured surface, roll out the dough to a thickness of about 1/8 to 3/16 inches. The dough should be pliable and easy to work with but firm enough to hold its shape.
Using a 1½-inch diameter circle cookie cutter, cut out circles from the rolled dough. Work swiftly to maintain the dough's firmness, transferring the cut circles to the bowl of sugar. Gently turn each circle over to ensure sugar adheres to both sides.
Place the sugared circles onto an ungreased cookie sheet, ensuring they are spaced about 1 inch apart. Use a fork to prick each circle about four times, which will help them bake evenly.
Continue cutting and transferring more circles until all dough is used. If the dough becomes too warm, return it to the refrigerator for a few minutes.
Bake the cookies in the preheated oven for 7 to 9 minutes, or just until they are set. Keep a close eye on them—don’t let them brown! Once done, allow them to cool on the pan for a few minutes before transferring them to a wire rack to cool completely.
While the cookies cool, prepare the filling. In the bowl of a stand mixer, beat the remaining unsalted butter until smooth and fluffy, about 2 minutes. Gradually add in the powdered sugar and vanilla extract, beating until the mixture is smooth and fluffy again, which should take another minute or two.
Divide the buttercream filling into two bowls. Tint one bowl with a little bit of green food coloring and the other with red food coloring. Aim for pastel colors rather than bright shades.
Transfer the buttercream filling into a piping bag fitted with a medium plain tip. If you don’t have a piping bag, simply cut off the end of a plastic bag to create an opening.
Pipe a generous layer of the buttercream onto the back side of one cookie. Carefully top it with another cookie, pressing gently to secure. If you prefer a casual look, you can spoon the filling onto the cookie instead of piping it.
