Pat 6 bone-in, skin-on chicken thighs dry with paper towels and season all over with 2 teaspoons of the kosher salt and 1/2 teaspoon black pepper.
Heat 1 tablespoon of the olive oil in a large heavy-bottomed pot or Dutch oven over medium-high heat until shimmering. Working in 2 batches, add the chicken skin-side down in a single layer. Sear until the skin is crisp, golden-brown, and releases easily from the pan, 3 to 4 minutes per side. Transfer to a large plate or baking sheet; the chicken will not be cooked through.
Reduce the heat to medium. Heat the remaining 1 tablespoon olive oil in the pot until shimmering. Add 1 diced medium yellow onion, 8 ounces quartered cremini mushrooms, and the remaining 1 teaspoon kosher salt. Cook, stirring occasionally, until softened, about 8 minutes. Stir in 3 minced garlic cloves and cook until fragrant, about 30 seconds.
Stir in 1 tablespoon tomato paste, 4 fresh thyme sprigs, and 2 bay leaves. Cook until darkened in color and fragrant, 2 to 3 minutes. Stir in 1 tablespoon plus 1 1/2 teaspoons all-purpose flour and cook for 1 minute to remove the floury taste.
Stir in 1 cup dry white wine. Scrape up any browned bits from the bottom of the pot and cook until the wine is reduced by half, about 2 minutes.
Stir in 1 cup low-sodium chicken broth and 1 diced medium Roma tomato, and bring to a boil. Reduce the heat to maintain a gentle simmer. Return the chicken to the pot skin-side up so that it is mostly submerged (some overlapping is OK); pour in any accumulated juices from the plate. Cover and simmer until the chicken is very tender, about 30 minutes.
Remove and discard the thyme stems and bay leaves. Taste the sauce and season with more kosher salt and black pepper as needed. Garnish with chopped fresh parsley leaves if desired.