Add the flour, baking powder, baking soda, and salt to a mixing bowl and stir to combine.

In the bowl of a stand mixer fitted with a paddle attachment, mix the shortening and sugar together on medium-high speed until soft and fluffy.

With the mixer running, add the eggs one at a time.

Add the sour cream and vanilla and mix until creamy.

Reduce to low speed and add the dry mixture 1/3 at a time until evenly mixed.

Chill the dough in the fridge for 1-2 hours.

Divide the dough into two halves.

Roll the first half out on a floured surface until it's a little over 1/4" thick.

Cut out cookies with a floured cookie cutter, and use a spatula to transfer them to the baking sheet.

Repeat with the other half of the dough, then bake the cookies at 350°F for 10-12 minutes, or until just beginning to brown around the edges.

Move cookies to a cooling rack to cool completely.

Prepare the frosting, adding powdered sugar or a splash of milk as necessary to achieve thick, fluffy frosting.

Spread the frosting generously over the cookies and top with sprinkles.