Preheat the oven to 425°F (220°C).
Pat the chicken thighs dry with paper towels. In a small bowl, mix together 2 teaspoons kosher salt, 1 teaspoon black pepper, and 1 teaspoon smoked paprika. Rub the spice mixture evenly over both sides of the chicken thighs.
Heat 2 tablespoons olive oil in a large oven-safe skillet over medium-high heat. Add the chicken thighs skin-side down and sear for 5-7 minutes until the skin is golden brown and crispy. Flip the chicken and cook for an additional 3 minutes.
Transfer the skillet to the preheated oven and roast the chicken thighs for 20-25 minutes, or until the internal temperature reaches 165°F (74°C). Remove from oven and let rest.
While the chicken roasts, place the peeled and chopped potatoes and garlic cloves in a large pot. Cover with cold water and add 1 teaspoon kosher salt. Bring to a boil over high heat, then reduce to a simmer and cook until the potatoes are tender, about 15-20 minutes.
Drain the potatoes and garlic and return them to the pot. Add 4 tablespoons butter and 1/2 cup whole milk. Mash until smooth and creamy. Season with 1 teaspoon kosher salt and 1/2 teaspoon black pepper. Keep warm.
Bring a medium pot of water to a boil. Add the trimmed green beans and cook for 4-5 minutes until tender-crisp. Drain and immediately transfer to a bowl of ice water to stop cooking and preserve color. Drain again.
In a medium skillet, melt 1 tablespoon butter over medium heat. Add the green beans and sauté for 2 minutes. Season with 1/4 teaspoon kosher salt and 1/4 teaspoon black pepper. Remove from heat.
Serve the roasted chicken thighs alongside the garlic mashed potatoes and sautéed green beans.