Whisk the flour, baking powder, and salt in a large bowl. Set aside.
Beat the butter and cream cheese with the sugar in the bowl of your stand mixer fitted with the paddle attachment until smooth. Scrape down the sides and mix in the eggs, one at a time. Add the vanilla and beat to combine. Scrape down the sides again if needed and add the flour mixture in three additions with the speed on low. Cover the dough and chill 2 hours until firm.
Make sure your oven racks are sent to the middle top and middle bottom slots and preheat the oven to 350 degrees F. Line two baking sheets with parchment paper and set aside.
Roll the dough into 1 1/2" balls and roll in the graham cracker crumbs to coat. Arrange on the baking sheets, 2 inches apart. Using the back of a tablespoon, make an impression in the center of each cookie for the cherry filling. Place 3 cherries in the center of each.
Bake in preheated oven for 12 to 14 minutes, rotating once halfway through cook time, until cookies have begun to crack and are light golden.
Let cool for 10 minutes on baking sheets before transferring to a wire rack to cool completely.
Because of the cream cheese, it is best to store leftover cookies in the fridge for up to 3 days.