In a small saucepan over medium heat, melt the butter together with the mint leaves. When the butter is completely melted and bubbly, turn off the heat. Set the pan aside and allow the mint to steep, 30 minutes. Using a fine mesh sieve, strain the butter.
To the bowl of a stand-mixer fitted with the paddle attachment, add the butter and sugars. Beat on medium-high speed 2 minutes. Add the egg and vanilla, beating until incorporated. Next add the flour, baking soda, and salt. Mix again until combined, scraping the sides and bottom of the bowl as needed. Add the chocolate chips and mix briefly, about 30 seconds. Refrigerate the dough 1 hour.
Preheat oven to 350 degrees. Line two large baking sheets with parchment paper. Using a medium cookie scoop, scoop the dough onto the baking sheet, about 6-8 cookies per sheet, leaving plenty of room for the cookies to spread out. Bake the cookies in the preheated oven for 10-12 minutes, or until golden on the edges but still somewhat undone in the center. Allow to cool on a wire rack for 10 minutes. Repeat with any remaining dough.
Cookies are best served warm or room temperature. Store in an airtight container.