In medium bowl, whisk together flour, baking powder and salt; set aside.
In a large bowl, beat sugar and butter with an electric mixer, until light and fluffy. Add eggs one at a time, beating after each addition, then add vanilla. Gradually add the flour mixture, beating on low speed, just until incorporated.
Divide dough into 3 equal portions. Shape one portion into a 4 x 4-inch square, wrap in plastic wrap and place in the refrigerator; this will be the “white” portion of the cookie.
Return one portion to the bowl and beat in red food coloring, adding more to reach desired color. Shape into a 4 x 4-inch square, wrap in plastic wrap and place in the refrigerator. Repeat steps with the last portion of dough, adding green food coloring, to reach desired color. Refrigerate all of pieces of dough for 1 hour.
Remove the dough from the refrigerator. Cut each square in half to make two rectangles. Wrap half of each color in plastic and place back in the refrigerator. Roll out “white” dough between two pieces of wax paper until the rectangle is about 1/8-inch thick. Repeat with red and green rectangles.
Peel the wax paper off one side of the red dough. Peel the wax paper off one side of the white dough. Lay the red dough on top of the white dough and peel back the wax paper off the red dough. Peel the wax paper off one side of the green dough and lay on top of the red dough. Remove the wax paper from the other side of the green dough.
Starting at the short end, roll all three layers tightly together to form a log. Repeat the stacking and rolling process with the remaining dough in the refrigerator.
Pour sprinkles onto a baking sheet with sides. Roll the logs in sprinkles, pressing them into the log as you roll. Wrap the logs in wax paper and then in plastic wrap, refrigerate for 1-2 hours.
Remove the logs from the refrigerator and roll them on the counter several times to remove the flat side. Refrigerate until ready to bake.
Preheat the oven to 350 degrees, and line 2 baking sheets with parchment paper.
Remove the logs one at a time, and slice into 1/4-inch rounds. Place the rounds about 2-inches apart on the baking sheet. Bake for 9-11 minutes, until puffed and lightly golden (not brown).
Cool on baking sheets for 10 minutes then transfer to a cooling rack to cool completely.
Store the pinwheels in an airtight container.
Cook's Note: The dough will be sticky, do not add more flour as the cookies will be tough. Keeping the dough refrigerated makes it easier to shape and cut the cookies.