Season thighs with salt and pepper. Heat oil in a large skillet over medium-high and brown thighs skin-side down, 5–7 minutes; flip and cook 2 minutes. Remove to a plate.
Lower heat to medium, add onion and cook 4–5 minutes until soft. Stir in garlic and cook 30 seconds.
Pour in crushed tomatoes, broth, oregano, and red pepper flakes; scrape browned bits from pan.
Nestle chicken back into sauce, skin-side up. Simmer gently, uncovered, 25–30 minutes until internal temp reaches 165°F and sauce thickens.
Stir in basil and butter off heat. Taste and adjust salt. Serve over rice, pasta, or mashed potatoes.