In a mixing bowl, beat butter with electric mixer on low speed or by hand until creamy, then blend in the egg. Slowly add dry cookie mix and blend until all incorporated. Gather dough into a ball and flatten into a disc. Wrap dough in plastic and freeze for 20 minutes, until firm.
Preheat oven to 350 degrees and line a baking sheet with parchment paper. Remove dough from freezer and form into tablespoon sized balls. Place cookies 2" apart on the baking sheet and bake for 13-15 minutes, until the edges of the cookies begin to turn golden. Cool on the baking sheet for 5 minutes then move to a wire rack and cool completely.
Working with 6-7 cookies at a time, break apart into a blender and pulse until they become the texture of sand. Repeat with remaining cookies, place crumbs in a bowl and set aside.
To make the frosting, in a small bowl, blend together the butter and yogurt until smooth. Add the dry frosting mix and blend until creamy. Using a spatula, spread frosting around the rim of four mason jars. Dip the frosting covered rims into the sugar cookie crumbs and sprinkle with natural rainbow sprinkles. Set in freezer.
Place frozen strawberries, ice cream and milk in the blender and pulse until smooth. Pour 1 1/2 cups of the sugar cookie crumbs into the blender and pulse a few times to incorporate. Remove glasses from freezer and divide the milkshake evenly between the four glasses. Top with whip cream and leftover sugar cookie crumbs.