Preheat the oven to 350 degrees F (175 degrees C). Line a 9×13″ baking pan with parchment paper, and spray parchment paper with non-stick spray.
Mix 1 1/2 cups sugar, flour, cocoa powder, salt, and baking powder together in a mixing bowl.
Mix butter, the 3 whole eggs, and vanilla extract together in a separate bowl; add butter mixture to the bowl with the flour mixture and stir batter until well mixed.
Pour the batter into the prepared baking pan and set aside.
Using a stand or hand mixer, beat the softened cream cheese, 1/4 cup sugar, egg yolk, mint extract, and food coloring at medium speed until everything is well mixed and the color is nice and even.
Place dollops of the green mint topping on top of the brownie batter in the pan. Using a butter knife held upright, dip through the dollops and into the batter, then drag the knife to one side of the cake pan to create a swirled marbling effect with the green and brown. Repeat in rows, then do the same going up and down until you’ve got a nice swirl pattern.
Bake in the preheated oven until edges are brown and center is set, about 30 minutes.
Remove pan from the oven and let brownies cool completely, about 30 minutes.
Remove the brownies from the pan by lifting the parchment paper (with brownies) out of the pan. Using a shamrock-shaped cookie cutter, cut shamrocks out of the brownies. You can serve immediately, or store in the refrigerator until ready to eat.