Season chicken pieces generously with salt and pepper on both sides. Heat olive oil in a large skillet over medium-high heat until shimmering, then add chicken and sear 3-4 minutes per side until golden brown. Remove chicken to a plate; don't worry about cooking through completely since it finishes in the sauce.
In the same skillet, melt butter with remaining oil over medium heat. Add diced onion and sauté 5 minutes until softened and translucent, stirring occasionally. This onion base builds flavor foundation for the entire cozy creamy spinach chicken recipe.
Stir in minced garlic and cook 1 minute until fragrant, being careful not to burn it. Add thyme, oregano, nutmeg, and a pinch of black pepper, toasting the spices 30 seconds to wake up their flavors.
Pour in chicken broth and use a wooden spoon to scrape up any browned bits stuck to the pan bottom—those are pure flavor. Return chicken to skillet, bring to simmer, and cook 15-18 minutes until chicken reaches 165°F internally.
Whisk cornstarch with 1 tbsp water to create a slurry, then stir into the simmering liquid to thicken slightly. Add cream cheese in chunks and heavy cream, stirring constantly 2-3 minutes until cream cheese melts completely and sauce becomes silky smooth.
Gently fold in fresh spinach in batches, letting each addition wilt into the creamy sauce before adding more. Cook 3-4 minutes total until all spinach is tender and vibrant green throughout.
Taste and adjust seasoning with additional salt and pepper if needed. Stir in Parmesan cheese and let simmer 1 minute to meld flavors, then remove from heat and serve immediately.