Heat a large skillet or Dutch oven over medium heat. Add the extra virgin olive oil and allow it to heat up.
Add the finely chopped garlic and diced onions to the skillet. Cook for 2-3 minutes until the onions are translucent and the garlic is fragrant.
Stir in the crushed red pepper flakes and cook for an additional minute.
Add the diced bell peppers, sliced mushrooms, diced carrots, and diced zucchini to the skillet. Cook for about 5-7 minutes until the vegetables are slightly tender.
Sprinkle the dried thyme, dried basil, dried Mexican oregano, and kosher salt over the vegetables. Stir well to combine.
Pour in the tomato and olive puree and stir to coat the vegetables evenly. Reduce the heat to low and simmer the sauce for 30-45 minutes, stirring occasionally.
While the sauce is simmering, cook the spaghetti according to the package instructions until al dente. Drain the pasta and set it aside.
Once the sauce has simmered and the flavors have melded together, turn off the heat and let it sit for 5-10 minutes.
Add the sliced grilled chicken breast to the sauce and stir gently to coat the chicken.
Divide the cooked spaghetti among plates and top with the chicken and sauce mixture.
Sprinkle grated Parmigiano Reggiano cheese over each plate.
Serve the Chicken & Spaghetti Cacciatore immediately.