Boil a large pot of salted water and cook the pasta according to package directions until al dente; reserve 0.5 cup of pasta water, then drain the pasta.
Season the chicken strips with salt, black pepper, and dried oregano.
Heat olive oil in a large skillet over medium-high heat; sear the chicken until golden brown and the internal temperature reaches 165°F (74°C). Remove chicken from the pan and set aside.
In the same skillet over medium heat, add the minced garlic and chopped sun-dried tomatoes; sauté for 1 to 2 minutes until fragrant.
Pour in the heavy cream and bring to a gentle simmer.
Whisk in the grated Parmesan cheese until the sauce is smooth and slightly thickened.
Add the fresh baby spinach and red pepper flakes; stir until the spinach is completely wilted.
Return the cooked chicken to the skillet and add the cooked pasta; toss thoroughly to coat in the sauce.
If the sauce is too thick, add the reserved pasta water 1 tablespoon at a time until the desired consistency is achieved.
Serve immediately, garnished with additional Parmesan if desired.