Bring a large pot of water to a boil.
In the meantime, heat oil in a large skillet over medium heat. Add onion and garlic and sauté until tender and translucent. Stir in remaining prepared vegetables, except the leafy greens. Season with two pinches of sea salt and a few grinds of black pepper and sauté until just tender, about 5 minutes.
To the pot of boiling water, add kosher salt and pasta. Cook pasta according to package instructions.
Into the skillet pour in the chopped tomatoes and beans and simmer ten minutes. Sprinkle with another pinch of sea salt. Stir in chopped greens and fresh herbs and cook until wilted.
When pasta is cooked until al dente, remove two cups of pasta cooking water and reserve. Drain the pasta and add it to the skillet with the vegetables and toss. Add enough pasta water to coat the vegetables and the pasta. Taste for seasoning and serve with grated cheese if desired.