Sauté zucchini in 1 Tbsp. hot oil in a large skillet over medium-high heat 5 minutes or until zucchini begins to brown. Add garlic, red pepper, and 1/4 tsp. kosher salt; cook, stirring often, 4 to 5 minutes or until garlic begins to brown. Remove from skillet.
Add tomatoes, black pepper, and remaining 1 Tbsp. oil and 3/4 tsp. kosher salt to skillet; cook, stirring occasionally, 2 minutes. Cover, reduce heat to medium, and cook, stirring occasionally, 10 minutes or until tomatoes begin to burst.
Cook pasta according to package directions; drain, reserving 1/4 cup hot pasta water. Add pasta, hot pasta water, and zucchini mixture to skillet along with basil and parsley; toss. Top with cheese.