Place racks in middle and lower third of oven; preheat to 350°. Toast ½ cup blanched hazelnuts on a rimmed baking sheet, tossing once, until golden brown, 8–10 minutes. Let cool, then coarsely chop; set aside. Increase oven temperature to 375°.
Generously coat 2 large rimmed baking sheets with extra-virgin olive oil. Cut 1 large head of savoy cabbage (about 3 lb.) in half through core; cut each half into 6–8 wedges, keeping core intact.
Toss 6 oz. Gruyère, coarsely grated (about 1½ cups), and 1 Tbsp. cornstarch in a medium bowl to combine. Bring 1⅔ cups heavy cream, 2 Tbsp. Dijon mustard, 2 garlic cloves, finely grated, 1 tsp. finely grated lemon zest, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 1 tsp. freshly ground pepper to a simmer in a medium saucepan. Add Gruyère mixture a handful at a time, whisking after each addition until melted. Cook sauce, whisking constantly, until thick enough to coat a spoon, about 1 minute. Remove from heat. Taste cheese sauce and season with more salt and/or pepper if needed.
Working with one wedge at a time, brush cabbage on all sides with about half of cheese sauce. Sprinkle very generously on all sides with 5 oz. Parmesan, finely grated (about 3 cups), pressing to adhere. Divide wedges, cut sides down, between prepared baking sheets, spacing at least 1" apart.
Roast cabbage until beginning to brown on top, 30–35 minutes (don’t fret if stray bits of cheese on baking sheet burn slightly). Turn wedges over and rotate baking sheets top to bottom and front to back. Continue to roast until golden brown in spots on the other side, 20–25 minutes longer.
Meanwhile, mix ¼ cup finely chopped parsley, reserved toasted hazelnuts, and remaining ½ tsp. finely grated lemon zest in a small bowl to combine. Season with salt and pepper.
Heat broiler. Consolidate cabbage on one of the baking sheets and broil on upper rack, watching closely, until dark brown and charred in spots, about 3 minutes.
When ready to serve, heat remaining cheese sauce over medium, whisking often and loosening with a splash or so of cream if needed, just until steaming, about 2 minutes. Spread sauce in a shallow serving dish or on a platter and arrange cabbage wedges on top. Scatter parsley mixture over, then top with more Parmesan.