"These are especially fun for kids to make--they'll love squishing the dough balls together to make each marble. Cream cheese gives the cookies richness and chewiness. Just make sure both the butter and cream cheese are at room temperature before you start so that they'll incorporate fully into the dough. The food coloring is optional. Omit it if you like-or add more if you prefer a more vibrant green."
Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with a silicone baking mat or parchment paper.
Put 1 3/4 cups sugar, butter, cream cheese, baking powder, salt, and peppermint and vanilla extracts in a bowl. Cream together with a mixer until well blended, 2 or 3 minutes. Mix in egg until incorporated. Add 2 cups of the flour; mix on low speed until incorporated, 2 to 3 minutes (dough will be very soft).
Divide dough roughly in half and transfer one half to another bowl. Mix in food coloring, if using, and remaining 1/2 cup flour into one half of dough. Mix cocoa powder into other half. Place 1/2 cup sugar in a small bowl.
Pinch off about 1 teaspoon of green dough and roll into a small ball; repeat with remaining green dough. Do the same with chocolate dough. To make each cookie, line up 4 small balls of dough in a row, alternating colors: green, chocolate, green, chocolate. Squish the 4 small dough balls together and roll lightly into 1 big ball. Roll in sugar; set on prepared baking sheet, leaving 2 inches between cookies. Repeat with remaining dough.
Bake until cookie edges start to turn golden brown, 13 to 15 minutes. Cool on baking sheet 10 minutes. Transfer to a wire rack to cool completely.