Whisk together 2 1/2 cups flour, cocoa powder, baking soda, salt, and baking powder in a large bowl until thoroughly mixed.
Beat in white sugar, 2/3 cup butter, water, 1 teaspoon vanilla extract, and eggs to make a smooth batter.
Place chocolate chips into a bowl and mix with 2 tablespoons flour until the chips are coated; fold chocolate chips into the batter.
Divide batter between the prepared muffin cups, filling each cup about 2/3 full.
Bake in the preheated oven until a toothpick inserted into the center of a cupcake comes out clean, about 20 minutes. Remove from oven and let cool completely.
While cupcakes are cooling, beat 1 cup butter, Irish cream liqueur, 2 teaspoons vanilla extract, and green food coloring with an electric mixer in a large bowl until mixture is smooth, thick, and evenly colored.
Reduce mixer speed to low and beat in confectioners' sugar, 1 cup at a time, until frosting is desired consistency. Beat in more confectioners' sugar to make a stiffer frosting.