Pat the chicken thighs dry with paper towels and season generously with salt and pepper on both sides.
Heat a large skillet over medium-high heat and add olive oil, letting it shimmer and just start to smoke.
Carefully place the chicken in the pan, skin-side down if using skin-on, and sear without moving for about 6-8 minutes until the underside is deep golden and crispy.
Flip the chicken and cook for another 5 minutes until it's cooked through and registers 75°C (165°F) internally.
Remove the chicken from the pan and set aside. Reduce the heat to medium and add the minced garlic to the same pan, sizzling for about 30 seconds until fragrant and slightly golden.
Stir in the grated Parmesan cheese and cook, stirring constantly, until it melts and the mixture becomes glossy and aromatic, about 2 minutes.
Add the butter and a splash of lemon juice, swirling the pan until the sauce is smooth, shiny, and fragrant.
Return the chicken to the pan, spooning the sauce over the pieces, and cook for another minute to reheat and meld the flavors.
Remove from heat and let the chicken rest for 3-5 minutes. Plate the chicken, spooning extra sauce over the top for a glossy, cheesy finish.