This pasta toss is inspired by a similar dish at Franny's restaurant in Brooklyn. The cabbage caramelizes in the pan and becomes just tender enough to bind with the pasta without losing its toothsomeness. Fresh red chile is a must for a pop of color and heat--don't skip it.
Bring a large saucepan filled with water to a boil. Add pasta; cook 7 to 9 minutes or until al dente. Drain in a colander over a bowl, reserving 1/4 cup cooking liquid.
Heat a large skillet over medium heat. Add oil; swirl to coat. Add garlic to pan; sauté 30 seconds or until beginning to brown. Remove garlic from pan with a slotted spoon; set aside. Increase heat to medium-high. Add cabbage to pan; cook 6 minutes or until browned and tender, stirring occasionally. Stir in salt, black pepper, and chile; cook 2 minutes. Stir in pasta, reserved 1/4 cup pasta cooking liquid, and reserved garlic. Stir in rind and 5 ounces cheese. Divide pasta mixture among 4 bowls. Sprinkle evenly with remaining 5 ounces cheese and thyme.