Beat the cold butter until smooth, then slowly mix in the heavy cream until combined. The mixture may look slightly curdled before it comes together.
Add the flour and salt, mixing just until a soft dough forms. Avoid overmixing to keep the cookies tender.
Divide the dough into two discs, wrap well, and chill for at least 30 minutes until firm but still easy to roll.
Roll one dough disc to about ⅛ inch thick on a lightly floured surface. Cut into small rounds and coat both sides with granulated sugar.
Place the cookies on a baking sheet and prick each one three times with a fork. This helps prevent uneven puffing while baking.
Bake at 375°F (190°C) for 7–9 minutes, until the edges are lightly golden but the tops remain mostly pale.
Let the cookies cool on the baking sheet for 2 minutes, then transfer them to a wire rack until completely cool and crisp.
Beat the softened butter with the vanilla and heavy cream, then gradually add the powdered sugar until smooth and fluffy.
Spread or pipe a small amount of buttercream onto one cookie and gently top with another cookie. Let the filling set for about 15 minutes before serving.