In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl with an electric hand mixer, beat the butter for 5 minutes until it’s fluffy and paler in color.
Add the flour and cream, mixing until just combined.
Form the dough into a ball and wrap tightly in plastic wrap. Chill in the refrigerator overnight.
When ready to bake, preheat the oven to 375°F. Line a rimmed baking sheet with parchment paper.
Place the sugar in a shallow pie plate or on a plate. Set aside.
Lightly flour a clean surface, counter or rolling mat. Working in batches, roll the dough to approximately 1/8-inch thickness. Cut the dough using a 1-inch circular cookie cutter. Transfer each cookie round to the sugar plate/dish. Flip, patting in the sugar.
Place them on the prepared baking sheet and prick them down the center 3 times with a fork.
Bake the cookies for 7-9 minutes, removing the cookies from the oven just before they start to brown. Allow to set for 1-2 minutes and then transfer them to a wire cooling rack. Allow them to cool fully before making into cookie sandwiches.
Filling:
In the bowl of a stand mixer fitted with the paddle attachment or a large mixing bowl with an electric hand mixer, beat the butter until light and pale, approximately 5 minutes.
Add the powdered sugar, vanilla, heavy cream and salt until smooth. It is too thick, add 1 teaspoon more heavy cream or milk.
If only doing one color, add a few drops of the desired gel food coloring and blend until smooth. If using multiple colors, divide the frosting filling and repeat with other colors.
If using a piping bag, fill the piping bag using a circle tip, then place a large dab in the center of one cookie, topping it with another to make a sandwich. If using an offset spatula, just place a teaspoon amount in the middle and smoosh together.
Allow the cookies to set then store in an airtight container with layers separated by parchment paper.