Season the chicken generously with salt and pepper and lightly coat with flour.

Heat a black steel pan (one that has a tight fitting cover) over high heat until very hot. Add 1 tablespoon of the oil and heat until the surface is rippling but not smoking. Working in batches to avoid crowding the pan, add 3-4 chicken thighs, skin side down, and lower the heat slightly, to medium-high. 

Weight down the thighs with a heavy plate (with additional weight added to plate) to create an even sear across the entire surface and cook for 5 to 6 minutes, until evenly golden but not too dark in any spots. Check after the first 1 to 2 minutes to ensure no black spots are forming and lower the heat as needed. Place the thighs, skin side up, in a single layer in the Dutch oven

Add the shallots and garlic to the skillet, cover and cook for 5 minutes over low heat to soften. Turn up heat, remove cover and cook for two minutes until golden brown.

Add the sherry and cook for 4 minutes to reduce,, then stir in the vinegar , honey and sugar and cook until slightly thickened. Stir in the stock, tomatoes, mustard and mushroom caps and season with salt and pepper.

Add the chicken and bring to a simmer. Insure that liquid rises to edge of chicken but does not cover or encroach on crispy skin

Cover and just simmer for 45-60 minutes. Transfer the chicken to a plate and keep warm.

Simmer the sauce until slightly thickened. Return the chicken to the sauce and serve.