Preheat oven to 450 degrees Fahrenheit.

Lay all the vegetables evenly on a Gefen Parchment-lined baking sheet. Drizzle with three tablespoons olive oil, kosher salt, one teaspoon lemon pepper, Parmesan cheese, and rice vinegar. Toss until evenly coated. Bake for 25 minutes, turning once midway.

Remove vegetables from oven and reduce heat to 350 degrees.

While vegetables are roasting, bring a six-quart pot of water to a boil. Prepare linguine according to package instructions, then drain.

Transfer pasta to a 9- x 13-inch (20- x 30-centimeter) baking pan. Add remaining three tablespoons olive oil, crushed garlic, one teaspoon salt, remaining half teaspoon lemon pepper, one cup shredded cheese, and roasted vegetables. Mix well. Sprinkle remaining cup of shredded cheese on top.

Cover pan and bake for 20 minutes. Serve immediately.