In a small saucepan, melt the butter over low heat. Remove from the heat and skim off the foam. Using a ladle, remove the clear melted butter, leaving the white milky solids behind; discard the solids. You should have 3/4 cup plus 2 tablespoons of clarified butter. Refrigerate the clarified butter until solidified, about 30 minutes.
Preheat the oven to 350°. In a bowl, beat the chilled clarified butter with a handheld mixer at medium speed until pale and fluffy, about 3 minutes. Sift in 1 3/4 cups of the confectioners' sugar and beat at low speed, scraping down the side of the bowl as necessary. Gradually beat in the flour just until incorporated. Using your hands, gently knead the dough until smooth. Cut the dough into 4 equal pieces.
On a lightly floured work surface, roll 2 pieces of the dough into 1-inch-wide logs. Slice the logs crosswise 1 inch thick. Arrange the slices on 2 cookie sheets, about 1 inch apart. Press the tines of a fork into each cookie to make a pattern. Bake in the upper and lower thirds of the oven for about 18 minutes, switching the sheets halfway through baking, until pale golden on the bottoms. Transfer the cookies to a rack to cool and repeat with the remaining dough.
Sift the remaining 1/4 cup of confectioners' sugar with the ground cloves generously over the cooled cookies.