Preheat the oven to 350°F (175°C) and line a muffin pan with cupcake liners.
In a mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt.
In a separate bowl, beat the softened butter and sugar until light and fluffy. Add the eggs one at a time, then mix in the vanilla extract.
Gradually add the dry ingredients and milk to the butter mixture, mixing just until the batter is smooth. Avoid overmixing.
Divide the batter evenly among the cupcake liners, filling each about two-thirds full.
Bake for 16–18 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Transfer the cupcakes to a wire rack and allow them to cool completely before decorating.
For the frosting, beat the softened butter until creamy. Gradually add the powdered sugar, then mix in the vanilla extract and heavy cream.
Add blue gel food coloring gradually and beat until the frosting reaches a bright Cookie Monster blue color.
Transfer the frosting to a piping bag fitted with a star or grass piping tip. Pipe textured frosting over each cupcake to create a fluffy Cookie Monster fur effect.
Place two candy eyes near the top of each cupcake.
Gently press a mini chocolate chip cookie into the lower part of the frosting to create the Cookie Monster cookie-in-the-mouth look.
Serve the Cookie Monster Cupcakes immediately or store them in an airtight container until ready to enjoy.