Preheat oven to 325º F. Cream 1 cup of the butter and the sugar until fluffy. Add the yolk and 1 tablespoon of vanilla. Blend in. Stir in the flour. Roll the dough into balls--1 tablespoon of dough for each cookie--and place the balls about 2 inches apart on an ungreased cookie sheet. Squish them down with the bottom of a glass dipped in flour, until they reach about 2 1/2 inches across. Bake about 12 minutes. Let them sit on the sheets for 1 minute, then remove them to cool on a rack.
Mix the frosting while they're cooling. Stir together sugar, 1/4 cup butter, the cream, and 1 tablespoon of vanilla. The mixture should be thick but spreadable. When the cookies are cool, spread about 2 rounded teaspoons on half the cookies and press another cookie on top of each. Yum!