Pat your chicken breasts dry with paper towels. This step matters more than you think. Wet chicken won't sear—it'll steam. Season both sides generously with salt, pepper, oregano, and thyme.
Heat olive oil in a large skillet over medium-high heat. When it shimmers, lay the chicken breasts in the pan. Don't move them. Let them sear for 5-6 minutes until golden brown. Flip and sear the other side for another 5-6 minutes. The chicken doesn't need to be cooked through yet. Transfer to a plate.
In the same skillet, melt butter over medium heat. Add your diced onion and cook for 3 minutes until it softens. Add minced garlic and cook for another 60 seconds. You should smell that garlic—that's when you know it's working.
Sprinkle the flour over the onion and garlic. Stir constantly for 1 minute. This creates a roux that'll thicken your sauce and make it silky instead of watery.
Pour in the chicken broth and stir, scraping the brown bits off the bottom of the pan. Those bits are liquid gold. Add the sun-dried tomatoes and stir everything together. Let it bubble for 2 minutes.
Return the chicken to the skillet. Pour the heavy cream over everything. Reduce heat to medium and simmer for 10-12 minutes. The chicken will finish cooking in the cream, and the sauce will thicken up beautifully.
When the chicken is cooked through (165°F in the thickest part), stir in the fresh spinach and Parmesan cheese. The spinach will wilt in about 2 minutes. The cheese will melt and make the sauce even creamier. Taste it and adjust salt and pepper if you need to.
Let everything sit for 2 minutes before serving. This helps the sauce set up and the flavors settle.