Preheat oven to 350 degrees F. Line a 9x13" rectangular pan with foil, extending the sides of the foil over the edges of the pan. Spray the foil with cooking spray and set aside briefly.
Combine the butter, powdered sugar, and flour together with an electric mixer until a soft dough comes together. Press the dough evenly into the prepared pan. Bake for approx. 8-10 minutes.
While crust pre-bakes, steep the mint. Combine the rum and mint leaves (or, if using rum extract, rum extract, water, and mint leaves) and steep in a bowl while the crust bakes. Then make your filling: In a medium bowl, whisk together the eggs, sugar, flour, and salt until creamy and pale yellow. Whisk in the lime zest, juice, and milk, followed by the green food coloring, if using. Lastly, strain the mint leaves and add the liquid from the mint leaves to the filling mixture, stirring to combine.
Pour the filling evenly over the crust and return to the oven. Bake for an additional 20-25 minutes or until the center is just about set - if it jiggles a little, that's okay, but it shouldn't be sloshing in the pan. Remember, do not over bake these! Cool the bars in the pan completely, then refrigerate for at least 1-2 hours before cutting for cleaner squares. Garnish with additional powdered sugar, if you'd like.