Season the chicken breasts with salt and freshly ground black pepper on both sides. Heat the olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for about 5-6 minutes per side or until golden brown and cooked through. Remove the chicken from the skillet and set aside.

In the same skillet, melt the butter over medium heat. Add the minced garlic and chopped shallot. Sauté for 2-3 minutes until fragrant and the shallots become translucent.

Pour in the chicken broth to deglaze the skillet, scraping up any browned bits from the bottom. Allow it to simmer for about 1-2 minutes.

Reduce the heat to low, then slowly stir in the heavy cream. Add the Pecorino Romano and Parmesan cheeses gradually, stirring constantly to help the cheeses melt and blend smoothly into the sauce.

Stir in the dried oregano and fresh thyme leaves. Add the chopped sun-dried tomatoes, allowing them to soften and infuse the sauce with their flavor.

Return the cooked chicken breasts to the skillet, spooning the creamy sauce over them. Let it simmer for 3-4 minutes, allowing the flavors to meld and the chicken to reheat.

If desired, add a handful of baby spinach or arugula, stirring gently until just wilted. This will add a fresh, earthy contrast to the dish.

Garnish with extra fresh thyme leaves and a grated Pecorino Romano cheese sprinkle. Serve hot, paired with crusty bread, pasta, or steamed vegetables to soak up the creamy sauce.