Preheat oven to 350 degrees.

Sift together flour, sugar, baking powder, and salt. Add cold butter pieces, then use a pastry cutter to incorporate the butter into the dry ingredients until the mixture resembles coarse crumbs.

Pour in the heavy cream, stirring gently with a fork until the dough just comes together. Use your hands to press it into a ball in the bowl (dough will be crumbly) then turn it onto a floured surface. (You can add a tiny bit more cream if needed. Gently press into a circle with your hands, then use a rolling pin to roll the dough to about 1/2 inch thick.

Use a small round biscuit cutter to cut circles of dough, then transfer them to a baking sheet. Bake for 16 to 18 minutes, or until barely golden brown. Allow to cool completely, then make the glaze.

GLAZE Mix together the 1/2 cup milk and vanilla. Pour it into a bowl with the sifted powdered sugar and the salt. Whisk until totally smooth. When the biscuits are totally cool, dunk them in the glaze to coat, then place them on a cooling rack so that the excess will drip off. Allow to set completely, then serve! (Sugar biscuits will keep several days.)