Cream the butter and sugar until fluffy. Beat in the egg and both extracts.
Whisk the flour, baking powder, and salt; mix into the wet ingredients to form a dough.
Divide the dough into thirds. Tint one portion red, one green, and leave one plain.
Roll each portion into a rectangle about 1/8 inch thick between sheets of parchment.
Stack the layers (plain on the bottom, red in the middle, green on top), trimming to even rectangles. Starting from a long edge, roll tightly into a log. Wrap and chill 2 hours.
Preheat the oven to 350°F. Slice the log into 1/4-inch rounds and place on parchment-lined sheets.
Bake 8 to 10 minutes, until just set (do not brown). Cool on the sheet 5 minutes, then move to a rack.