Prepare Chicken: Cut each chicken breast horizontally so it's half as thick as before, resulting in 4 thinner pieces (Note 5). Pat them dry with paper towels. Generously season both sides of each chicken piece with salt and pepper.
Sear Chicken: Heat 10-inch sauté pan over medium to medium-high heat until hot. Add olive oil to cover pan, and place chicken breasts in single layer over oil. Cook until each side is golden brown, 4 to 5 minutes per side. When chicken is cooked through, transfer to large plate. Work in batches if your pan is not large enough to hold all at once.
Make Sauce: Reduce to low heat. Add heavy whipping cream, butter, and parmesan cheese to pan. Stir until butter and cheese are melted, scraping up any browned bits on bottom of pan. Increase to medium heat and bring to simmer. Stir in spinach until wilted. Stir in minced garlic and oregano until well-mixed.
Return Chicken & Serve: Transfer chicken back to pan, leaving any liquid on plate, and simmer for 1 minute. Top with sun-dried tomatoes. Turn off heat. Serve (Note 6), and optionally top with additional grated parmesan cheese.
