Cook the pasta according to the package directions.
Meanwhile, heat 1 tablespoon of the oil in a medium sauté pan or skillet over medium-high heat until the oil shimmers. Add the onion and cook for 2 to 3 minutes, until it starts to soften; then add the squash and 1 tablespoon of the oil; season with salt and pepper to taste. Cook for 6 to 8 minutes, stirring every minute or so, until the squash softens and just starts to brown. If it browns too quickly, reduce the heat to medium.
Add the tomatoes and stir to combine. Cook for about 4 minutes or until the tomatoes are warmed through and have softened. Remove from the heat, then add the oregano and basil. Taste and adjust the seasoning; add a tablespoon of oil if needed.
Drain the cooked pasta and transfer to a large serving bowl. Add the sauce and toss to combine. Serve immediately, with Parmesan cheese, if desired.