Pat the chicken completely dry and season with 1 tsp of the salt and the pepper. Slice the onion, cut the peppers into 3 cm strips, and crush the garlic.
Heat the olive oil in a 28 cm / 11-inch Dutch oven over medium-high heat. Sear 4 chicken pieces skin-side down for about 6 minutes until deep golden, then flip for 1 minute and move them to a plate. Repeat with the remaining 4 pieces. Pour off all but about 2 tbsp of fat.
Lower the heat to medium. Add the onion and garlic and cook for 3 minutes, scraping up the browned bits. Add the peppers and the remaining 1/2 tsp salt, and cook for 5 minutes until the edges soften.
Pour in the wine and simmer for 2 minutes until the sharp smell fades. Add the crushed tomatoes with their juice and stir.
Return the chicken to the pot skin-side up, with any juices from the plate. Nestle the pieces into the peppers so the skin stays above the sauce. Cover and simmer gently over low heat for 20 minutes.
Uncover and cook over medium heat for 5 minutes, until the sauce looks glossy, leaves a trail when you drag a spoon through it, and a thigh reads 175 F / 80 C at the thickest part. Take the pot off the heat, scatter the torn basil on top, and drizzle with the extra virgin olive oil.