Heat oil in large skillet over medium-high heat. Add next 3 ingredients; sauté 1 minute. Add leeks; sauté until beginning to soften, about 4 minutes. Add diced tomatoes; stir 1 minute. Add wine and vinegar; bring to boil. Cover and cook until tomatoes break down, stirring often, about 5 minutes.
Meanwhile, cook pasta in large pot of boiling salted water until tender but still firm to bite. Drain, reserving 1 1/4 cups pasta cooking liquid.
Add pasta, 1/2 cup reserved pasta liquid, and 3/4 cup cheese to sauce in skillet. Toss over medium-high heat until sauce coats pasta, adding more liquid by 1/4 cupfuls if dry. Season with salt and pepper. Serve, passing 1 cup cheese separately.