Use a sharp knife to cut each chicken breast in half horizontally to create thinner cutlets, helping them cook evenly. Pat them dry with paper towels to remove excess moisture, which helps the cheese crust adhere better.
Place the shredded Asiago cheese in a shallow dish. Dip each chicken piece into the cheese, pressing gently to coat both sides evenly with a thick, cheesy layer. Set aside.
Heat a large skillet over medium heat and add the olive oil, letting it heat until shimmering and slightly rippling, which indicates it's ready for searing.
Add the coated chicken breasts to the skillet carefully, and cook for 4-5 minutes without moving them to develop a golden, crispy crust. Flip once the cheese starting to brown and the chicken releases easily from the pan.
Reduce the heat slightly and add the butter along with the minced garlic to the pan. As the butter melts, tilt the pan slightly and spoon the fragrant, bubbling butter over the chicken to enhance flavor and encourage even browning.
Cook for another 4-6 minutes, occasionally spooning the garlic-butter mixture over the chicken, until the chicken is cooked through and the crust is crisp and golden. Use a meat thermometer to check for an internal temperature of 165°F (74°C).
Transfer the chicken breasts to a serving plate and let rest for a couple of minutes. Meanwhile, tilt the pan to gather the sauce and cheese bits, allowing them to become thickened and slightly caramelized.
Spoon the thickened cheese and garlic butter sauce over the rested chicken, garnish with fresh herbs if desired, and serve immediately for a crispy, cheesy, and juicy dish with a rich aroma.
