Bring a large pot of salted water to a boil. Cook the spaghetti until al dente, about 10 minutes. Drain and rinse under cold water to prevent sticking, then set aside.
Combine the salt, pepper, oregano, and parsley in a small bowl. Season both sides of the chicken breasts with this mixture.
Place a large skillet over high heat and coat the pan with canola oil. Once hot, sear the chicken for 2 minutes per side (the chicken will not be fully cooked). Transfer the chicken to a plate and set aside.
Wipe out the skillet. Lower the heat to medium and return the pan to the stovetop. Preheat your oven's broiler to high.
Toss the cherry tomatoes in 1 tablespoon of olive oil and salt. Spread onto a baking sheet. Broil for 3 minutes to blister.
Add the blistered tomatoes, Italian gold tomato, Roma tomatoes, shallot, garlic cloves, and 1 tablespoon of olive oil to a food processor. Cover and pulse 4-5 times to lightly break apart the tomatoes.
Add 1 tablespoon of olive oil to the hot skillet and swirl to coat. Add the tomato mixture to the pan along with the vinegar. Season with a pinch of salt, pepper, and red pepper flakes. Stir and simmer for 7 minutes.
Add the chicken to the sauce. Cover the skillet and cook for 7 minutes until the chicken is cooked through.
Plate the spaghetti, top with pomodoro sauce and chicken. Garnish with fresh shredded parmesan and basil. Serve warm.
Notes
If you can't find Italian Gold tomatoes, you can use more Roma tomatoes instead.