Whisk the flour, baking powder, cinnamon, ginger, cloves, salt and baking soda in a medium bowl. Beat the brown sugar, molasses, melted butter and egg yolks in a large bowl with a mixer on medium-high speed until smooth, about 1 minute. Reduce the mixer speed to low; add the flour mixture and beat, gradually increasing the speed to medium high, until the dough comes together, about 3 minutes.
Roll out the dough between 2 pieces of parchment paper coated with cooking spray until 1/8 inch thick. Freeze until firm, 30 minutes.
Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment. Cut out cookies using 2-inch cutters; arrange 1 1/2 inches apart on the baking sheets. Gather the scraps and chill until firm, then reroll once to cut out more cookies. Refrigerate the cutouts until firm, 20 minutes.
Bake the cookies, switching the pans halfway through, until golden, 10 to 12 minutes. Let cool 2 minutes on the baking sheets, then transfer to racks to cool completely.
Make the icing: Beat the confectioners' sugar, meringue powder and 3 to 4 tablespoons water in a bowl with a mixer on high speed until smooth and thick. Transfer to a resealable bag and snip a small corner. Pipe onto the cookies and sprinkle with nonpareils. Let set 30 minutes.