Preheat oven to 350 degrees and line a cookie sheet with parchment paper. In a large bowl, beat butter with an electric mixer on low speed or by hand until creamy, then blend in egg. Slowly add dry cookie mix and blend until all incorporated.
Form dough into tablespoon sized balls and place 2” apart on prepared cookie sheet. Bake for 12-14 minutes, until the edges begin to turn golden. Cool on cookie sheet for 5 minutes, then move to a wire rack to cool completely.
In a large bowl, use your hands and break cookies into small pieces. Combine remaining ingredients in a large bowl and whisk together. To assemble popsicles, fill popsicles molds 1/3 high with orange juice mixture then top with 1-2 tablespoons of crumbled cookies.
Repeat with remaining ingredients until the popsicle mold is full, there may be leftover cookie crumbs. Freeze popsicles 40-50 minutes, then add popsicle sticks. Freeze another 1-2 hours or until frozen. When ready to serve, run warm water along popsicle mold to loosen the popsicles. Serve immediately.