Pat chicken dry and season both sides with salt and pepper.
In a large skillet, heat olive oil and 1 tablespoon of butter over medium-high heat.
Sear chicken cutlets for 5 minutes per side until internal temperature reaches 165°F (74°C), then remove from skillet and tent with foil.
Add remaining 1 tablespoon of butter to the skillet and sauté minced garlic for 60 seconds until aromatic.
Pour in chicken stock to deglaze the pan, scraping the fond from the bottom with a wooden spoon.
Incorporate crushed tomatoes, oregano, and red pepper flakes; simmer over medium heat for 8 minutes to reduce slightly.
Reduce heat to low and whisk in heavy cream and Parmesan cheese until a cohesive emulsion forms.
Return chicken and any accumulated juices to the skillet, simmering for 2 minutes to incorporate.
Garnish with fresh basil and serve immediately.