Pat the chicken breasts dry with paper towels, then season both sides generously with salt and pepper.
Heat olive oil in a skillet over medium-high heat until shimmering and just starting to smoke.
Carefully place the chicken breasts in the hot skillet, laying them away from you to avoid splatters. Sear for about 4-5 minutes per side until golden brown and cooked through, then transfer to a plate and set aside.
Reduce the heat to medium and add minced garlic to the same skillet, stirring constantly until fragrant, about 30 seconds. Be careful not to burn the garlic.
Pour in the heavy cream, scraping up any browned bits from the bottom of the pan to loosen their flavor.
Sprinkle grated asiago cheese into the sauce, stirring slowly until the cheese melts fully, creating a smooth, cheesy sauce.
Add dried thyme and season with more salt and pepper as needed. Let the sauce simmer gently for 2-3 minutes until slightly thickened and silky.
Return the seared chicken breasts to the skillet, nestling them into the creamy sauce. Spoon some sauce over the top, then cover and simmer on low heat for 5 minutes, allowing flavors to meld.
Uncover the skillet, check that the chicken is heated through and the sauce has thickened to a silky consistency. Taste and adjust seasoning if needed.
Plate the chicken breasts, generously spooning the Asiago cheese sauce over each piece. Garnish with a sprig of thyme or additional cheese if desired.
Serve hot alongside your favorite sides, such as roasted vegetables or mashed potatoes, and enjoy the rich, cheesy flavor.
