Generously season the chicken breasts on both sides with salt and freshly cracked pepper.
Heat a large skillet over medium-high heat. Add the olive oil and unsalted butter. Once melted, add the seasoned chicken breasts and cook for 5-7 minutes on each side until browned and cooked through. Remove from skillet and set aside.
In the same skillet, lower the heat and add the minced garlic. Sauté for about 30 seconds until fragrant.
Add the halved cherry tomatoes to the skillet and cook for 2-3 minutes until softened.
Stir in the fresh spinach leaves and cook for another 1-2 minutes until wilted.
Reduce heat to low, pour in the heavy cream, and stir to combine. Gradually add the Parmesan cheese and dried Italian herbs, stirring until smooth and creamy.
Return the cooked chicken breasts to the skillet, ensuring they are well-coated with the sauce. Simmer for an additional 2-3 minutes.
Taste the sauce and adjust seasoning with more salt, pepper, or herbs if necessary.
Remove from heat and garnish with fresh basil leaves if desired. Serve immediately.