Preheat a nonstick (not Belgian) waffle iron.

Cream butter and sugar in a medium bowl. Beat in eggs and vanilla. Add flour, cocoa powder, oil and espresso powder (if using). Beat until thoroughly combined.

Drop the batter by rounded teaspoonfuls about 1 inch apart onto the preheated ungreased waffle iron. (To avoid burnt fingers, use two spoons, one to scoop and one to scrape dough onto the waffle iron.) Close and cook until the cookies are puffed and cooked through, 1 to 1 1/2 minutes. Waffle irons vary, so watch closely and don't let the cookies get too dark. Transfer to a wire rack to cool until just warm. Dust the cookies with confectioners' sugar while still slightly warm (see Variations). Variations: Instead of confectioners' sugar, drizzle cooled cookies with melted bittersweet and/or white chocolate. Or make a peppermint drizzle: Mix 1 cup confectioners' sugar, 4 teaspoons water and 1/4 teaspoon peppermint extract; add natural green food coloring, if desired.

MAKE AHEAD TIP: Store in an airtight container for up to 1 day. Dust with additional confectioners' sugar just before serving.