In the mixing bowl of a stand mixer, using the Whisk attachment, add the Butter, Sugar, Vanilla, and Egg, and blend until light and fluffy.  

In a separate bowl, add the Flour, and Baking Powder, and stir well to blend.  Add the Flour a little at a time and mix on low to blend, until all the Flour is added.  Remove the Whisk attachment, and use the paddle. 

Continue to blend the Cookie dough until it's completely blended and a smooth ball starts to form.  Scrape down the mixing bowl as needed.

Line two cookie sheets with Parchment paper, and roll the cookie dough into small balls, about 1 inch balls, and place the balls on the Parchment paper.

Bake at 350 degrees for about 15 minutes, or just until the cookies start to turn a light golden brown around the edges.  About half way through baking the cookies, check the oven, and the cookies may have started to crack a little.  Take a flat bottom glass, dip it in Sugar before lightly applying to each cookie - smash the cookies very gently, and slightly, making them a little flatter, and spread out a little more.  This will give the cookies the crinkle look. 

When the cookies are done, remove from the oven to a wire rack to cool completely. 

While cookies are cooling, make the Frosting.

Add the Powdered Sugar to a bowl, and add the Milk a little at a time.  Stir well while adding the Milk, until the Frosting is smooth, and no lumps are visible.  If the Frosting is thin, add a little more Powdered Sugar until it's thick enough to ice the Cookies. 

When you have the right consistency, place a couple of Tablespoonfuls in a separate bowl, and add a drop or two of the Black Food Coloring Gel.  Stir well to blend, and if the Black Frosting thinned a little, add a little Powdered Sugar to achieve a thicker consistency. 

Frost the Cookies with the White Frosting, and allow them to sit for about 45 minutes until the Frosting is set on the Cookies.  Place the Black Frosting in a pastry bag with the small tip, and pipe the Black Frosting onto the White Frosting, using a back and Forth motion, to resemble a string or strand for the Lights. 

Place the mini M&M's along the Black Frosting, so it appears as a strand of Colored Lights on the Cookies. 

Serve, and Enjoy!