Whisk together the flour, baking powder, salt, and cloves in a small bowl. Beat the butter and sugar in a large bowl with an electric mixer at medium-high speed until pale and fluffy, about 3 minutes in a standing mixer (preferably fitted with paddle attachment) or 6 minutes with a handheld beater. Beat in the egg and vanilla. Reduce speed to low, then add flour mixture and mix until just combined.
Form dough into a 12-inch log (2 inches in diameter) on a sheet of plastic wrap and roll up in the plastic wrap. Chill dough in the refrigerator for 1 hour.
Cut 1/2-inch thick slices from the log with a sharp knife and arrange on 2 ungreased large baking sheets, about 1-inch apart.
For basic sugar cookies, sprinkle generously with coarse sugar and bake for 15 minutes or until lightly browned and slightly puffed.
Cool on baking sheets for 3 minutes, then transfer with a metal spatula to racks to cool completely.
For Chocolate and Walnut Cookies:
Make basic dough according to recipe above, but adding the cocoa powder to the flour mixture and folding in the nuts just after mixing the batter. Bake for 15 minutes and then cool on sheets for 3 minutes before transferring to racks to cool completely.
For Almond-Orange Cookies:
Make basic dough according to recipe above, but adding both the orange zest and ground almonds when you add the flour mixture.
When cookies are formed, make a slight depression in the middle and fill each with about 1 teaspoon marmalade. Top each with a good pinch of sliced almonds. Bake for 20 minutes and then cool on sheets for 3 minutes before transferring to racks to cool completely.