Life-Changing Garlic Butter Chicken Thighs

3 pounds bone-in, skin-on chicken thighs (about 6 small)
1 1/4 teaspoons kosher salt, divided
4 cloves garlic
3 tablespoons unsalted butter
12 ounces fresh or frozen green beans

Arrange a rack in the middle of the oven and heat the oven to 425ºF.
Debone 3 pounds bone-in, skin-on chicken thighs: Flip each chicken thigh over so it is skin-side down. Using kitchen shears, cut through the meat along both sides of the center bone, making sure not to cut all the way through the meat and skin. Cut off the cartilage at the top and bottom of the bone. Cut underneath the bone, which will cut the bone off completely from the thigh. Use the shears to trim off any excess fat, cartilage, or skin.
Pat the chicken thighs dry with paper towels and season on all sides with 1 teaspoon of the kosher salt. If using fresh green beans, trim, then cut in half crosswise.
Place the chicken thighs skin-side down in a large (12-inch) oven-safe skillet, preferably cast iron, and turn the heat to medium. Cook undisturbed until the skin is golden and crispy, using tongs to move the thighs around the pan after 10 minutes to ensure even browning, 15 to 18 minutes total (they will not be cooked through at this point). Meanwhile, place 3 tablespoons unsalted butter in a small microwave-safe bowl and microwave on HIGH until melted, 30 to 45 seconds. Mince 4 garlic cloves and add to the melted butter.
Transfer the chicken skin-side up to a clean plate, leaving the rendered fat in the pan. Add 12 ounces green beans to the pan, season with the remaining 1/4 teaspoon kosher salt, and toss to coat the beans in the chicken fat. Place the chicken thighs skin-side up on the green beans.
Drizzle the garlic butter over the chicken and green beans and transfer the skillet to the oven. Roast until the chicken is deeply golden brown, crispy, and registers 160ºF in the thickest part, 12 to 15 minutes.