In the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl with an electric hand mixer, cream the butter and sugar together on medium speed until light and fluffy, about 3 minutes. Scrape down the sides of the bowl. Add the eggs, cream, and vanilla; beat until well combined.
1 cup unsalted butter, 1 1/2 cups granulated sugar, 3 large eggs, 1/2 cup heavy cream, 1 teaspoon vanilla
In a large bowl, whisk together the flour, baking soda, baking powder, salt, and nutmeg.
Gradually add the flour mixture to the butter mixture, mixing just until combined.
Divide the dough into half and pat into two disks. Wrap the disks in plastic wrap and chill in the refrigerator for at least 2 hours, but preferably overnight.
When ready to bake, preheat oven to 350°F. Line baking sheets with parchment paper.
On a well-floured work surface, roll one of the dough disks out to about 1/4-inch thick. The dough will be sticky, so dust the rolling pin and/or top of the dough with additional flour as needed.
Use floured cookie cutters to cut the dough into your favorite shapes. Transfer the shapes to the prepared baking sheets, placing the cookies about 1 inch apart. Re-roll the dough scraps as needed. Repeat with the remaining dough disk.
Bake the cookies for 10-12 minutes, or until lightly golden at the edges. Let cool on the baking sheet for 3-5 minutes, then transfer to a wire rack to finish cooling.
Make the frosting
In the bowl of a stand mixer fitted with the paddle attachment or in a large bowl with an electric hand mixer, beat the butter on medium speed until smooth. Add the powdered sugar and mix on low until combined.
Add the cream 1 tablespoon at a time until you reach your desired consistency for spreading on the cookies. Add the vanilla and mix until combined.
2 to 3 tablespoons heavy cream , 1/2 teaspoons vanilla extract
If desired, add food coloring to the frosting or divide into smaller bowls for multiple colors. Start with just 1 or 2 drops of food coloring, adding more as needed/desired.
Food coloring
Spread onto cooled cookies. If you wish to add sprinkles or decorating sugar, do so while the frosting is still wet, as it will crust up slightly as it sets.