Preheat your oven: Set the oven to 400°F
Marinate the chicken: In a large bowl, combine the chicken thighs, olive oil, Dijon mustard, and miso paste. Use your hands to rub the mixture all over the chicken, getting under the skin where possible.
Prepare the leeks: Remove the tough outer leaves (1-2 layers). Trim the root ends and tops of the dark tops. Cut each leek in half from top to bottom to expose the layers. This is key for washing them thoroughly.. Rinse under running water, gently fanning the layers without fully separating, to wash through the dirt. Pat dry and cut into 3–4 inch pieces. Set aside.
Sear the chicken: Heat 1 tablespoon olive oil in a 3.5-quart braiser or oven-safe skillet over medium heat. Place the chicken thighs skin side down. Sear for 7–10 minutes, until you are able to remove the chicken easily. If they are stuck, they aren't ready. Flip and cook another 5–7 minutes. Transfer to a plate.
Sauté the leeks: If there’s no rendered fat in the pan, add another tablespoon of olive oil. Arrange the leeks cut-side down (as best you can) and sauté for a few minutes. Pour in the broth and wine. Scrape up any flavorful brown bits stuck to the pan with a wooden spatula. Create a small well between the leeks and add the dijon and while grain mustards, and miso paste. Whisk them in the well to integrate them into the liquid, then stir to evenly distribute. Add salt and pepper to taste (give the broth a try first, as miso is inherently salty. If you want more, start with ¼ teaspoon each).
Braise: Return the chicken to the pan, skin side up, tucking the bottoms into the broth. Spoon the cannellini beans into the spaces between the leeks and chicken. Bake for 30–45 minutes, until the chicken is cooked through and the leeks are fork-tender.
Serve and enjoy. Serve hot with your choice of white rice, couscous, or crusty bread to soak up the sauce.