Bring a large pot of salted water to a rolling boil.
Season the diced chicken generously with kosher salt, fresh pepper, and the dried herb mixture (oregano and basil).
Heat a large skillet over high heat, spray lightly with cooking spray, then add the chicken and cook 3–4 minutes until no longer pink; remove and set aside.
Add the spaghetti to the boiling water and cook according to package directions; before draining, reserve about 1/2 cup of the pasta cooking water, then drain the pasta.
While the pasta cooks, return the skillet to high heat and add the olive oil.
Add the chopped garlic and sauté briefly until golden (avoid burning), then add the halved grape tomatoes, season with salt and pepper, reduce heat to medium-low, and cook about 4–5 minutes until tomatoes soften.
Add the drained pasta to the skillet with the tomatoes and toss to combine, adding reserved pasta water a little at a time if the mixture seems dry.
Return the cooked chicken to the skillet, add the chopped fresh basil, toss everything together to heat through, then serve with grated cheese if desired.