Bring a large pot of salted water to a boil. Add 8 ounces of penne pasta and cook according to package instructions until al dente. Drain and set aside, reserving about 1/2 cup of pasta water for later.
Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Add the diced chicken breasts, seasoning lightly with salt and pepper. Cook, stirring occasionally, until the chicken is cooked through and golden brown on the outside, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Then stir in the chopped artichoke hearts and fresh spinach. Cook, stirring, until the spinach wilts down and the artichokes are warmed through.
Lower the heat to medium and add the softened cream cheese and sour cream to the skillet. Stir constantly until the cream cheese melts smoothly into a creamy sauce. Gradually mix in the grated Parmesan cheese, salt, black pepper, and crushed red pepper flakes to taste. If the sauce is too thick, add reserved pasta water a tablespoon at a time until you reach your desired consistency.
Return the cooked chicken to the skillet, then add the drained penne pasta. Toss everything together until well combined and coated in the creamy sauce. Sprinkle the shredded mozzarella cheese over the top and cover the skillet for a couple of minutes to let the cheese melt.
Give the pasta a final gentle toss, then serve hot. Garnish with extra Parmesan or fresh herbs if desired. This dish pairs wonderfully with a light green salad or some crusty bread to soak up every last bit of sauce.