Step 1Place the flour on a plate and stir in 1 teaspoon salt and freshly ground black pepper. Pat the chicken thoroughly dry and dredge it in the flour, shaking off any excess.
Step 2Heat the oil in a large skillet over medium-high heat. When it’s hot enough that a piece of the chicken dipped in the oil sizzles, add the chicken, skin-side down. You’ll need to do this in two batches. Cook until the chicken has browned, 5 to 6 minutes, and then turn and cook on the other side until it no longer looks raw, 4 to 5 minutes. Remove the chicken to a plate and keep it warm.
Step 3Pour off all but about 2 tablespoons of the oil. Add the fennel and cook until it starts to become tender, about 3 minutes. Add the the shallots and cook until fragrant, about 2 minutes. Add the white wine and reduce by 1/3, until it smells sweet and not of raw alcohol, about 5 minutes. Stir in the mustard and add the mushrooms and green olives.
Step 4Add the chicken thighs back to the pan skin-side up, resting them on top of the fennel. Cover the pan, reduce the heat to medium-low and cook until the chicken is done through, about 10 minutes. Check by piercing a thigh deeply with a paring knife; the knife should slide in easily and there should be no bloody juices.
Step 5While the chicken is finishing, chop together the lemon zest and 2 tablespoons of the reserved fennel fronds.
Step 6Divide the fennel and mushrooms evenly among four warmed pasta bowls. Place the chicken on top and sprinkle with the chopped fennel fronds and lemon zest and a little more salt if necessary.