Pat thighs dry and season with salt and pepper. Heat oil in a large skillet over medium-high heat and brown chicken for 5 minutes per side; transfer to a plate.
Lower heat to medium and cook garlic, sun-dried tomatoes and oregano for 1 minute, stirring. Add broth and scrape up the browned bits.
Stir in cream and return chicken and its juices. Simmer gently for 6 to 10 minutes until the thickest meat reaches at least 165°F.
Stir Parmesan into the sauce around the chicken, then add spinach in two handfuls and cook for 1 to 2 minutes until just wilted.
Rest off the heat for 3 minutes and spoon the creamy tomato-spinach sauce around the thighs to serve.