Preheat the convection oven to 400°F (200°C) and line a heavy-gauge baking sheet with parchment paper.

Unroll the refrigerated pizza dough onto a clean, lightly floured work surface and divide into 8 equal-sized rectangles using a bench scraper or pizza cutter.

Position one mozzarella cheese stick at the short end of each dough rectangle.

Roll the dough tightly around the cheese, ensuring the lateral edges and longitudinal seams are pinched firmly to prevent cheese leakage during thermal expansion.

Combine the melted butter, minced garlic, and dried Italian seasoning in a small bowl; whisk until emulsified.

Arrange the rollups on the prepared baking sheet with the seam-side facing down, spaced at least 2 inches apart.

Apply the garlic butter mixture to the surface of each rollup using a pastry brush.

Bake for 10 to 12 minutes or until the internal dough is cooked and the exterior reaches a deep golden-brown color.

Remove from heat and immediately top with fresh parsley and grated Parmesan cheese while the surface fat is still liquid.

Rest for 120 seconds to allow the internal cheese to set slightly before service.