Bring a large pot of salted water to a rolling boil. Add the 10 oz. of uncooked spaghetti and cook until just shy of al dente, about 1-2 minutes less than package instructions. Drain and set aside.
Heat 2 tablespoons of olive oil or butter in a large skillet over medium-high heat. Add chicken pieces seasoned lightly with salt and pepper. Cook, stirring occasionally, until golden and cooked through, about 5-7 minutes. Transfer to a plate and set aside.
In the same skillet, add diced onion and sauté until translucent, about 3-4 minutes. Add minced garlic and cook for another 30 seconds until fragrant but not browned.
Reduce heat to medium-low, pour in 1 cup heavy cream or Half & Half. Stir to combine with onions and garlic. Add 1 tsp. dried oregano, ½ tsp. sea salt, ½ tsp. black pepper, and ½ tsp. red pepper flakes. Let sauce simmer for 3-4 minutes until slightly thickened.
Stir in ½ cup grated Parmesan and ½ cup grated cheddar cheese until melted and smooth. Return cooked chicken to skillet and stir to coat in cheesy sauce.
Add cooked spaghetti to skillet and gently toss to coat pasta in creamy sauce. Cook together for another 1-2 minutes to meld flavors.
Taste and adjust seasoning with salt, pepper, or red pepper flakes if needed. Serve hot, optionally garnished with extra Parmesan or fresh herbs.