In a large skillet, heat the 2 tablespoons of olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Add the chopped broccoli florets to the skillet. Season with kosher salt, pepper, and crushed red pepper. Sauté for 5-7 minutes until the broccoli is tender but still bright green. Remove from heat and allow to cool slightly.
In a mixing bowl, combine the sautéed broccoli mixture with the shredded mozzarella or Italian blend cheese. Stir until well combined.
Preheat your oven to 400°F (200°C). On a lightly floured surface, roll out the puff pastry to smooth out any creases.
Place the broccoli and cheese filling in the center of the puff pastry. Fold the edges over the filling, pinching them together to seal. You can also twist the ends for a decorative touch.
In a small bowl, beat together the egg and water. Use a pastry brush to apply the egg wash over the top of the pastry for a golden finish.
Transfer the assembled roll to a baking sheet lined with parchment paper. Bake in the preheated oven for 25-30 minutes, or until the pastry is golden brown and puffed.
In the last five minutes of baking, sprinkle the finely grated parmesan cheese over the top of the roll. Return to the oven until the cheese is melted and bubbly.