Prep. Preheat the oven to 350°F and position two racks in the center. Then, line two large baking sheets with parchment paper.
Cream butter and sugar. In a stand mixer fitted with the paddle attachment or a large mixing bowl using a handheld mixer, cream the butter and sugar together for 2–3 minutes until light and fluffy. Then, add the egg yolks and vanilla extract and beat for another 1–2 minutes until the mixture is pale and airy.
Add dry ingredients. In a small bowl, whisk together the flour and salt. Then, slowly add this dry mixture to the butter-sugar mixture, mixing at low speed after each addition until combined. Avoid overmixing to keep the dough tender.
Chill the dough. Cover the bowl tightly with plastic wrap and refrigerate for 30 minutes. Chilling will help the cookies hold their shape during baking.
Form the cookies. Use a cookie scoop or tablespoon to portion the dough, then roll each portion into a ball. Then, roll each ball in granulated sugar to create a lightly crisp exterior. Next, place the dough balls on the prepared baking sheets, spacing them one inch apart.
Indent the cookies. Press an indentation into the center of each dough ball using the back of a ¼ teaspoon or the handle of a wooden spoon. The indentation will spread slightly as the cookies bake.
Bake. Bake the cookies at 350°F for 12–14 minutes or until the edges are lightly golden. Transfer to a wire rack to cool completely before filling.
Make buttercream filling. While the cookies cool, make the buttercream. In a medium mixing bowl, beat the softened butter until smooth and creamy. Gradually add the powdered sugar, beating until fully incorporated and smooth. Add the vanilla extract and enough heavy cream or milk, one teaspoon at a time, to get a piping consistency. Add a few drops of food coloring and mix until evenly blended.
Assemble. Once the cookies are completely cool, pipe the buttercream into the indentations of each cookie using a piping bag fitted with a star or round tip. If you don’t have a piping bag, use a small spoon or a plastic bag with a snipped-off corner.
Serve and store. Allow the buttercream to set slightly before serving. Store cookies in an airtight container at room temperature for up to 3 days, or refrigerate for up to one week.