In a medium bowl, whisk together the vanilla instant pudding mix and cold whole milk until smooth and fully incorporated, about 1-2 minutes. The pudding will begin to thicken as you whisk. Add the bourbon and peppermint schnapps, stirring gently to combine. If using green food coloring, add it now and stir until you achieve an even color throughout. Let the mixture sit for 5 minutes to allow the pudding to fully set and the flavors to meld.
Using a rubber spatula, gently fold the thawed whipped topping into the pudding mixture in two additions until just combined. I like to fold rather than stir here because it keeps the mixture light and airy—vigorous stirring deflates the whipped topping and makes the final shots denser than they should be. Be gentle and stop folding as soon as no white streaks remain.
Divide the pudding mixture evenly among 15 small cups, shot glasses, or portion cups, filling each about three-quarters full to leave room for the garnish. Transfer the filled cups to the refrigerator and chill for at least 2 hours until fully set and cold.
Just before serving, top each shot with a small dollop of additional whipped topping and crown each with a fresh mint leaf. I like to gently slap the mint leaf between my palms first to release its oils and enhance that fresh mint aroma—it makes a real difference in the sensory experience. Serve immediately and enjoy chilled.