Season the chicken breasts generously with salt and pepper on both sides.
Heat olive oil and 1 tablespoon of butter in a skillet over medium-high heat until shimmering and bubbling.
Place the chicken breasts into the hot skillet, laying them away from you to prevent splatters. Sear for about 4-5 minutes until golden brown, then flip and cook another 4-5 minutes until cooked through and nicely browned.
Remove the cooked chicken to a plate and cover loosely with foil to keep warm; set aside.
Reduce the heat to medium, add the minced garlic to the same pan, and cook for about 30 seconds until fragrant and slightly golden, releasing its aroma.
Pour in the heavy cream, scraping up any browned bits from the bottom of the pan to incorporate flavor. Bring to a gentle simmer, stirring occasionally.
Stir in the shredded Asiago cheese, allowing it to melt smoothly into the cream, creating a rich, cheesy sauce. Let it simmer for 2-3 minutes until thickened slightly.
Return the chicken breasts to the skillet, spooning some sauce over the top. Let everything cook together for another 2 minutes, so the flavors meld and the chicken re-heats gently.
Taste the sauce and adjust with salt and pepper as needed, then turn off the heat.
Transfer the chicken to plates, spooning the creamy Asiago cheese sauce over each piece for a glossy, indulgent presentation.
Serve immediately, perhaps with a side of pasta or vegetables, to enjoy the full richness of the sauce.
