In bowl of stand mixer with paddle attached, beat butter until creamy smooth. Add heavy cream and mix on medium speed until smooth. Add flour and mix on low speed until incorporated, then flash on medium speed for five seconds to mix. Wrap dough in plastic wrap and refrigerate about 1 hour or until firm.
Preheat oven to 375ºF. Roll some of the dough to 1/8 inch thick on lightly powdered sugar surface (keep remaining dough refrigerated until ready to roll). Cut into desired shapes small cookie cutters (I used 1 1/2 inch tree shapes). Cut as many cookies as you can out of the first roll, then squeeze the dough together to roll and cut again. Your goal is to roll the dough the minimum amount of times. Finish that first chunk of dough before moving on to the next. Fill small bowl with granulated sugar and coat both sides of each cutout with sugar and then transfer to baking sheet (I found that a silicone covered metal baking sheet worked best). Prick each cutout with fork about 4 times.
Bake 7 to 9 minutes or just until set but not brown. Remove from cookie sheet to wire rack. Cool completely, about 1 hour.
Meanwhile, use a stand mixer with the whisk attached to cream butter for filling. Add powdered sugar and extract and mix on medium speed until smooth. It will be thick. Spread a thin layer (about 1/2 teaspoon) filling between bottoms of pairs of cookies.