In a stand mixer, cream together the pistachio pudding mix, unsalted butter, and granulated sugar until fluffy.
Scrape down the sides and beat in the egg.
Turn the speed down to low and mix in the all-purpose flour and salt until well-combined.
Spread dough onto parchment paper and roll dough to approximately 1/8-inch thick.
Transfer dough (on the parchment) to a cookie sheet and freeze for 20 minutes.
Remove from freezer and place parchment on counter. Cut out rounds using a 3-inch round cutter.
For half the cookies, cut out the center with a 1.5-inch clover cutter.
Bake in a preheated oven at 350°F for 6-8 minutes.
Let cookies cool on the baking sheet for 2 minutes before transferring them to a wire rack.
In a clean bowl, beat together softened butter and powdered sugar.
Add vanilla paste and milk and beat until fluffy.
Fit a pastry bag with an M2 tip and fill it with frosting. Pipe frosting onto the bottom of a full cookie.
Top frosted cookie with the clover-hole cookie and fill the hole with green sprinkles.
