Pat the chicken thighs completely dry with paper towels. This is crucial for crispy skin. Season both sides with 1 teaspoon salt and all the pepper. Let sit at room temperature while you prep the remaining ingredients.

Heat olive oil in a large oven-safe skillet over medium-high heat until shimmering. Add chicken skin-side down and cook without moving for 6-7 minutes until the skin is deeply golden and releases easily from the pan. Flip and cook 2 minutes more. Transfer to a plate; the chicken will not be fully cooked.

Pour off all but 2 tablespoons of fat from the pan. Reduce heat to medium and add the smashed garlic. Cook 1 minute until fragrant and just starting to color. Add white wine and scrape up any browned bits with a wooden spoon. Simmer for 3 minutes until reduced by half.

Stir in chicken broth, lemon zest, lemon juice, and remaining 1/2 teaspoon salt. Nestle the chicken back into the pan skin-side up, along with any accumulated juices. Scatter 2 tablespoons oregano around the pan. Roast at 425F for 20-25 minutes until the thickest part of the thigh registers 175F on an instant-read thermometer.

Transfer the chicken to a serving platter and tent loosely with foil. Remove and discard the garlic cloves. Bring the pan juices to a simmer over medium heat and reduce for 2-3 minutes until slightly thickened. Remove from heat and swirl in the cold butter until glossy. Taste and adjust seasoning.

Spoon the sauce over the chicken and sprinkle with the remaining fresh oregano. Serve immediately with crusty bread to soak up every drop.