Bring a large pot of salted water to a boil.

Place heavy skillet over medium heat and pour olive oil into hot skillet; add green onions and anchovy fillet. Cook and stir until anchovy breaks down and green onions are tender, 2 to 3 minutes. Add garlic to skillet and cook until translucent, about 1 minute.

Stir zucchini into green onion mixture; cook, stirring occasionally, until zucchini slices just start to become tender, about 2 minutes. Sprinkle with salt and black pepper; cook until zucchini centers start to change color to slightly green, 1 to 2 more minutes.

Pour tomato sauce and chicken stock into skillet. Reduce heat to low; add sugar. Mix jalapeno, Fresno, yellow mini pepper, and orange mini pepper rings into mixture. Bring sauce to a simmer and reduce heat to low.

Pour rotelle pasta into boiling water and cook, stirring often, until pasta is still slightly firm, about 7 minutes. Drain and let pasta stand for 2 minutes.

Bring sauce to a boil; stir in rotelle pasta. Reduce heat to medium. Cook, stirring often, until pasta, zucchini, and peppers are tender, 2 to 3 more minutes. Taste and adjust levels of salt and black pepper. Mix in about 1 1/2 teaspoon parsley. Serve in bowls and top with Parmigiano-Reggiano cheese and remaining 1/2 teaspoon parsley.