In a mixing bowl, combine the garlic herb cheese spread, shredded Colby-Jack cheese, and shredded Italian cheese blend. Mix well until all the ingredients are thoroughly combined. Set aside.
Preheat your oven to 375°F (190°C).
Open the tube of refrigerated breadsticks and unroll the dough into a long rectangle. Pinch the seams together to create a uniform surface.
Spread the cheese mixture evenly over the dough, leaving a small border around the edges.
Starting from one end, roll the dough up tightly to form a log.
Slice the rolled dough into 1-inch thick pieces, yielding about 12-15 roll-ups.
Place the roll-ups on a baking sheet lined with parchment paper. Brush the tops with the lightly beaten egg.
Sprinkle the shredded Parmesan cheese on top of each roll-up.
Bake in the preheated oven for 15-18 minutes or until golden and bubbly.
Remove from the oven and let cool for a few minutes before serving.
