For the ice cream: Soften the ice cream at room temperature until it is spoonable but not melting, about 20 minutes. Transfer it to a large bowl and drizzle with the bourbon. Work it into the ice cream with a wooden spoon. Then cover the bowl with plastic wrap and freeze until hard, 3 to 4 hours.
For the cookies: Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
Whisk together the flour, baking powder, baking soda and salt in a medium bowl until combined. Set aside. Beat together the butter and both sugars in a large bowl with an electric mixer on medium-high speed until the mixture is light and fluffy, about 5 minutes. Beat in the vanilla and eggs until creamy, 1 to 2 minutes. Add the flour mixture, reduce the mixer speed to medium-low, and beat until just combined. Stir in the chocolate chips.
Scoop 2 ounces of dough per cookie (about 3 tablespoons or a medium-size ice cream scoop) onto the baking sheets, about 3 inches apart. Bake, rotating the trays front to back and top to bottom halfway through cooking time, until lightly browned and the edges are set, 10 to 13 minutes. Cool a few minutes on the trays, and then transfer to a wire rack to cool completely. Line the trays with new parchment paper and bake the remaining cookies.
Scoop a very generous mound of ice cream (about 2/3 cup) onto one cookie and top with a second cookie. Repeat with the rest of the cookies and ice cream. Enjoy immediately.