Beat the softened butter and the powdered sugar together until they look light and creamy. There's no need to sift the powdered sugar unless it's got big lumps. If you do end up sifting it, make sure you you pack it down when you measure it.
Add a half-teaspoon of lemon extract and mix it in. Peel the banana and break it into chunks. Mix them in until they're thoroughly mashed and the powdered sugar and butter mixture is smooth again. Sprinkle in the baking powder and salt, and mix them in thoroughly.
Add the flour in half-cup increments, mixing after each addition. When the cookie dough si thoroughly mixed, take the bowl from the mixer and set it on the counter.
Mix in the chocolate chips by hand. You'll want them as evenly distributed as possible. Line your cookie sheets with foil and spray the foil lightly with Pam or another nonstick cooking spray.
Use a teaspoon to drop cookie dough 2 inches apart on the cookie sheets, no more than 12 cookies to a sheet. Use a metal spatula or the palm of your impeccable clean hand to flatten the cookies.
Bake the cookeis at 400 degrees for 8 to 210 minutes or until they're golden on top. Remove them from the oven and let them sit on the cookie sheet for 2 minutes. Then pull the foil off and transfer cookies, foil and all, to a wire rack to cool completely.