Make the cookies: In a medium bowl whisk together flour, baking powder, cream of tartar, baking soda, and salt.
In the bowl of an electric mixer fitted with a paddle attachment, beat the butter and sugar at medium speed until light and fluffy, about 3 to 4 minutes. Add the vanilla paste and egg and beat until fluffy.
Reduce the mixer speed to low, and slowly add the dry ingredients into the wet ingredients. The dough will be thick (you may have to finish incorporating the mixture with a spatula).
Place the 1/4 cup sprinkles in a bowl. Scoop up 2 tablespoons of dough and roll into a ball. Dip the ball in the bowl of sprinkles to cover lightly. Put the balls on a plate. Repeat with the remaining sprinkles and dough. Chill the dough for at least 2 hours.
Place racks in the center and upper third of the oven and preheat the oven to 350 degrees F. Line 2 baking sheets with Tovolo Silicone Baking Mats.
Transfer the chilled dough balls to the prepared baking sheets, leaving about 2 inches of space in between each ball.
Bake until the cookies have spread and are just beginning to brown around the edges, but are mostly pale and soft, 8 to 10 minutes. Let cool on the cookie sheets for 5 minutes before transferring to wire racks to cool completely. The cookies will keep in an airtight container for up to 4 days.
Peanut butter buttercream: Add butter, peanut butter and powdered sugar to a mixing bowl and combine on low speed.
Add vanilla paste and salt, then slowly add heavy cream. Beat until fluffy and smooth!
To assemble, line up like-size COOLED cookies and scoop a generous tablespoon of buttercream onto one cookie. Use the Tovolo® Scoop & Spread to spread the peanut butter buttercream move evenly onto the cookie. Atop with the second cookie and gently squeeze together. Any leftover buttercream is yours to eat without anyone being the wiser.
Eat at will!