In a large Dutch oven or heavy stockpot, heat the oil over medium-high heat. Season the chicken on all sides with salt and place in the pan smooth-side down. Cook the chicken until nicely browned, about 4 minutes per side. Remove to a plate and set aside.
Add the butter to the pan, if using, along with the onion. Sauté, stirring infrequently, until the onion has begun to brown and crisp, about 8 minutes. Remove half the onions from the pan and set aside.
Stir in the cabbage and mushrooms and continue to sauté until soft, about 5 minutes more. Season with 1 teaspoon salt and pour in the wine, if using, scraping up any brown bits from the bottom of the pan. Mix in the beans and arrange in an even layer.
Return the chicken to the pot, nestling it into the bean mixture. Add 4 cups of water, making sure that the chicken pieces are submerged. You can add more if necessary. Bring to a simmer and cook over medium-low heat, undisturbed, until the chicken easily breaks apart into pieces when pressed with a spatula, 30-40 minutes.
Off the heat, stir in the spinach, half the dill, lemon juice and mustard. Allow the stew to sit for a few minutes so the spinach becomes fully wilted. Taste the broth for seasoning and add more salt as necessary.
To serve, ladle the stew into bowls and garnish with the reserved dill and crispy onions.