Bring a large pot of water to a boil. Cook pasta until just tender, 4-5 minutes or according to package instructions.
Meanwhile, place 1 tbsp oil and garlic in a large skillet. Cook over medium heat, stirring occasionally, until the garlic is sizzling and fragrant, 2-5 minutes. Add sweet potato, bell pepper, tomatoes and water and cook, stirring occasionally, until the bell pepper is tender-crisp, 5-7 minutes. Remove from the heat; cover and keep warm.
Drain the pasta, reserving 1/2 cup of the cooking water. Return the pasta to the pot. Add the vegetable mixture, the remaining 1 tbsp oil, parsley, tarragon, vinegar, salt and cheese. Toss well. Add the reserved pasta water, 2 tbsp at a time, to achieve the desired consistency.