Combine the flour, baking powder, salt and sugars in a food processor and process briefly to mix. Add the butter in pieces; process with on/off bursts until the mixture has the consistency of cornmeal. Add the vanilla and process until the mixture just forms a ball.
Divide the dough into 2 equal portions then return one of the portions to the food processor. Add the strawberry extract, food coloring, and the extra tablespoons of flour to the processor and process until just incorporated.
Roll out each portion of dough between sheets of waxed paper. You want a rectangle about 11 × 8½ inches by ⅛ inch thick. Leave the dough between the sheets of waxed paper and slide onto a baking sheet. Refrigerate until firm, for at least 2 hours or up to 3 days.
Remove dough pieces from refrigerator. Pour the nonpareil decors into a shallow rectangular dish (such as a 9 × 13-inch pan.
Peel off the top sheet of waxed paper from both doughs. Brush the vanilla dough very lightly with water. Using the waxed paper, lift the strawberry dough and flip it onto the vanilla dough so they are stacked. Press with your fingertips to seal the two doughs together. Remove the top sheet of waxed paper and trim the edges even.
When the dough is just pliable (but still cold), roll up the dough(begin with the long side) like a jellyroll. As you begin to roll, gently curl the edge with your fingertips so you don’t get any air pockets as you roll dough into a log. As you roll, the vanilla portion may want to tear, pinch tears together as they happen and keep rolling.
After forming the dough into a log, throw away the waxed paper. Gently lift the log on top of the nonpareil decors in the dish and roll until the log is completely coated with decors. Wrap the log in plastic wrap and refrigerate until firm enough to slice (from 4 hours to a week, or freeze for up to 2 months; defrost in the refrigerator overnight before slicing).
Heat oven to 325°. To bake, slice the log into ⅛- to ¼-inch-thick cookies and bake on parchment-lined baking sheets for 15 to 17 minutes, until the cookies are no longer shiny on top and the bottoms of the vanilla portion are golden.
Keyword rainbow nonpareils, slice-and-bake cookies