In a large mixing bowl, use a hand mixer to beat together butter and powdered sugar until light and fluffy. Add in vanilla extract and beat until combined.
Add in flour and mix just until flour disappears. Fold in mini chocolate chips.
Transfer dough to a gallon-sized resealable plastic bag, or place between two layers of plastic wrap. Roll until 1/4 inch thick. Refrigerate on a flat surface until firm, about 1 to 2 hours.
Remove dough from plastic and use a butter knife to cut into equal-sized squares or rectangles. Transfer cut pieces to a parchment lined baking sheet.
Bake at 325 degrees for 18-20 minutes, until edges are just lightly kissed with brown.
Melt dipping chocolate in a small microwave safe bowl by microwaving on high for 30 seconds at a time, stirring between. Dip cookies in chocolate covering 1/3 or 1/2 of the cookie and transfer to parchment paper to harden.