Beat the softened butter and sugar together in a large bowl using an electric mixer on medium speed for 3-4 minutes until light and fluffy.
Add the eggs one at a time, beating well after each addition, then mix in the vanilla extract until fully combined.
Add the green gel food coloring to the wet mixture and mix until you achieve a bright Grinch-green color.
Whisk together the flour, baking powder, and salt in a separate bowl.
Add the dry ingredients to the wet ingredients and mix on low speed until just combined, being careful not to overmix.
Divide the dough into two portions, flatten each into a disk, wrap in plastic wrap, and refrigerate for 30 minutes.
Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
Roll out one disk of dough on a floured surface to 1/4 inch thickness and cut into circles using a cookie cutter.
Place cookies on prepared baking sheets, leaving 2 inches between each cookie, and decorate with red sprinkles arranged in heart shapes.
Bake for 8-10 minutes until the edges are set but the centers still look soft.
Cool cookies on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.
Repeat with remaining dough, re-rolling scraps as needed.