Season the chicken breasts on both sides with salt and black pepper.
Heat olive oil and butter in a large skillet over medium-high heat.
Add the chicken breasts and sear for 4–5 minutes per side until golden and cooked through. Remove and set aside.
Reduce heat to medium-low and add garlic to the same skillet. Cook for about 30 seconds until fragrant.
Pour in the heavy cream, stirring to scrape up any browned bits.
Add the grated Asiago cheese and simmer gently for 2–3 minutes until the sauce thickens slightly.
Return the chicken to the skillet and spoon sauce over the top. Simmer for 2 minutes.
Taste and adjust seasoning, then serve hot with sauce spooned over each piece.