Bring a large pot of salted water to a boil and cook the linguine according to package directions until al dente. Reserve 1/2 cup of the cooking liquid, then drain the pasta and set aside.
Slice each chicken breast horizontally into two thinner cutlets. Season both sides with salt, pepper, and 1 teaspoon of the dried oregano.
Heat the olive oil in a large nonstick skillet over medium-high heat. Add the chicken and cook about 4 minutes per side, until cooked through and no longer pink. Transfer the chicken to a plate and set aside.
If needed, add a little more oil to the skillet, then sauté the diced onion over medium heat until softened, about 3–4 minutes. Add the minced garlic and cook 1 minute more until fragrant.
Reduce heat to low and add the cubed cream cheese and half-and-half to the skillet. Stir and cook until the cream cheese melts and the sauce is smooth.
Stir in the crumbled feta, lemon juice, the remaining 1 teaspoon dried oregano, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Add the spinach, sliced sun-dried tomatoes, sliced kalamata olives, and sliced roasted red peppers; cook briefly until the spinach wilts.
Slice or chop the cooked chicken and return it to the skillet. Add the drained pasta and toss to combine, adding reserved pasta cooking liquid a few tablespoons at a time if the sauce needs thinning.
Transfer to a serving bowl, sprinkle with chopped fresh parsley, and serve immediately.
