Preheat your oven to 450F or 425F convection.
Trim off excess skin from the chicken and pat the skin dry (see video). Season the skins and flesh with about 1 teaspoon salt (about ¼ teaspoon per thigh). In a large (12”) oven-proof skillet (cast-iron is best) over medium heat, warm the olive oil and swirl it to coat the pan. Place chicken skin-side-down in the skillet. Let cook undisturbed until golden brown, about 7-10 minutes. Flip and cook for 1 more minute. Transfer the chicken to a plate (it will finish cooking in the oven).
Meanwhile, whisk together the water, mustard, and lemon. Set aside.
In the same skillet over medium heat, add the leeks and ¼ teaspoon salt and cook until softened, stirring occasionally, about 2 minutes, scraping up any bits of chicken that might be stuck to the pan.
Add the potatoes, garlic, and remaining ½ teaspoon of salt and cook for 1 minute, to soften the garlic and potatoes. Spread into an even layer and add the mustard liquid, then turn off the heat. Nestle the chicken thighs into the skillet, skin-side-up. Transfer to the oven for 20-25 minutes, or until the liquid has reduced and potatoes are cooked (we still want a little liquid in there!). Sprinkle the peas into the skillet, and return to the oven for 2 more minutes.
While the chicken braises, in a small bowl mix together the fennel and/or celery, vinegar, water, and salt. Set aside.
Serve with a side of fennel/celery and top with a generous squeeze of lemon and fresh herbs.