In the bowl of a stand mixer (or with a hand mixer), beat the butter 3-5 minutes until it's light and fluffy. With the mixer on low, slowly add the flour and then the cream. Mix until just combined. Cover and refrigerate the dough for at least two hours or overnight.
Preheat oven to 375 degrees F.
On a lightly floured surface, roll out the dough to a 1/8-inch thickness. Cut with a small tree-shaped cookie cutter. (Alternatively, you can use any style of cookie cutter you prefer.)
Add the sugar to a separate small bowl. Press the cut out trees into the sugar. Then, place on an ungreased cookie sheet. Prick with a toothpick or fork.
Bake 7-9 minutes, removing the cookies from the oven just before they start to brown. Remove them from the cookie sheet to cool.
In the meantime, make the filling. In the bowl of a stand mixer (or with a hand mixer), cream the butter and salt until light and fluffy (This will take 3-5 minutes.) With the mixer on low, add the powdered sugar, 2 tablespoons of heavy cream, and vanilla. Then add the food coloring. If the filling seems too thick, add more heavy cream until desired consistency is achieved.
To easily frost the cookies, put the filling in a piping bag. Once the cookies are cool, pipe the filling on the back of one cookie. Top with another cookie and press to secure.
Pack and store in an airtight container.