Place miniature tartlet tins, each about 1 ½ inches (4 cm) in diameter, on 2 rimmed baking sheets. Lightly brush each tin with the butter. Sprinkle generously with sanding sugar. Firmly press 1 rounded tablespoon of dough into each prepared tin, filling it three-fourths full.
Bake 1 batch at a time until the edges are set and the cookies feel firm to the touch, but have not yet taken on any golden color, 16–18 minutes. Let cool on the sheets on wire racks for 5 minutes. Using tongs if the tart tins are still warm, invert the tins and gently tap to remove the cookies. Use a metal spatula to transfer the cookies to the wire racks and let cool completely, about 30 minutes.
Dust the cooled cookies with confectioner’s sugar and serve right away; the cookies are best eaten the same day they are made.