Preheat your oven to 375°F (190°C). Line two large baking sheets with parchment paper or silicone baking mats to prevent sticking.
In a large mixing bowl, whisk together the melted unsalted butter, eggs, vegetable oil, peppermint extract, and green gel food coloring until the color is vibrant and uniform.
Add the vanilla cake mix to the wet ingredients. Use a spatula or hand mixer on low speed to combine until a soft dough forms. Do not overmix.
Place the dough in the refrigerator for 15 to 20 minutes. Chilling the dough makes it easier to handle and helps create a better 'crinkle' texture during baking.
Place the powdered sugar in a small shallow bowl. Using a small cookie scoop, portion the dough into 1-tablespoon sized balls.
Roll each dough ball between your palms to smooth it, then roll it thoroughly in the powdered sugar until heavily coated.
Place the coated dough balls on the prepared baking sheets, spaced at least 2 inches apart to allow for spreading.
Bake for 8 to 10 minutes. The cookies should be puffed and the edges set, but the centers should still look slightly soft. Do not overbake or the green color may brown.
Immediately after removing the cookies from the oven, gently press one red heart sprinkle into the side of each warm cookie.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.