Put the cherries, pistachios and brown sugar in a food processor and pulse until a fine crumb forms (take care not to over process or the filling will clump together). Set aside.
Put the butter and granulated sugar in the bowl of a stand mixer fitted with a paddle attachment and beat on medium-high until light and fluffy, about 2 minutes. Add the eggs, baking powder and salt and beat for another minute. Lower the speed to medium and add the flour, 1/2 cup at a time; beat until smooth. Cover and place in the fridge to chill, about 1 hour.
Divide dough the in half and flatten each into squares. Put one portion of dough in between two 12-by-12-inch sheets of parchment paper dusted with flour. Roll out into a 1/8-inch-thick square. Remove the top parchment sheet and sprinkle half of the cherry-pistachio filling evenly across the dough. Pat into an even layer. Tightly roll into one large log (using the parchment to help you). Trim the ends and then roll the exterior in a mixture of sprinkles to coat. Repeat with the remaining dough, filling and sprinkles. Tightly cover in fresh parchment and refrigerate overnight (preferred) or at least 4 hours, until the dough is firm.
Preheat the oven to 375 degrees F and line 2 baking sheets with parchment or a silicone baking mat.
Remove and uncover the dough logs and slice with a very sharp knife into 1/4-inch-thick pinwheels. Arrange about 1 inch apart on the prepared baking sheets. Bake until slightly golden, 8 to 10 minutes. Let the cookies cool on a wire rack. Store for up to 3 days in an airtight container, or freeze cookies for future use, up to 2 weeks.