Occasionally, the carrots will stay stubbornly crisp if you just add them to the pan. Here’s how to fix that. Take the cut up carrots, put them in a microwaveable container with a little water and nuke them for 3 minutes. If you don’t fear tough carrots, just add them when you add the wine to the pan.
Season both sides of the chicken with salt, pepper and half the Herbes de Provence, pressing lightly to help it stick. Dredge chicken in flour and shake off excess. I generally put a couple of heaping soupspoonsful of flour in a plastic bag, add the chicken, twist the top shut and shake it. Nice and easy.
Heat oil a large, deep skillet or sauté pan over medium-high heat. Add chicken in a single layer, skin side down. Cook until skin is golden brown, 6 to 7 minutes, then turn and brown the other side, 3 to 5 minutes. Transfer chicken to plate and reduce heat to medium. Pour off all but 2 tablespoons of fat (honestly, I seldom need to do this).
Add onion and cook, stirring frequently, until it softens and becomes translucent, 3 to 5 minutes. Stir in remaining Herbes de Provence. Stir in garlic and cook for about 30 seconds, until it becomes fragrant.
Add wine, stirring and scraping up any browned bits from the skillet. Add carrots to the pan, draining them if you microwaved them. Return chicken to the pan skin side up along with any juices, nestling the pieces among the carrot chunks. Add a cup or so of water, as needed. The chicken should not be covered by the liquid, but just sit in it. This keeps the skin a nice golden color, instead of turning it all pale and stewlike. Tuck in the bay leaves. Reduce the flame to medium-low, cover the pan and let it simmer, checking occasionally to make sure nothing is sticking or burning. If the liquid is cooking down too much, add a little water, but do so sparingly. After for 20 to 25 minutes, test the chicken with an instant read thermometer; it should register at least 160ºF for the chicken to be cooked through.
And now for the sauce. To thicken the sauce—or to make more sauce if it’s reduced down too much—here’s how. Remove the chicken to a plate. In a small bowl dissolve 1 tablespoon of cornstarch in 2 tablespoons of cold water, stirring carefully and working out lumps against the side of the bowl—any lumps in the mixture will become lumps in your sauce. Spoon a little sauce from the pan into the cornstarch mixture to warm it up. Spoon in some more. Seriously. Then slooooowly drizzle the cornstarch mixture into the sauce, stirring constantly, to avoid lots of nasty little lumps from forming in the sauce. You’ll see the sauce thickening. Return the chicken to the pan to let it warm through again.
Serve. Plate the chicken thighs along with a serving of rice next to it. Spoon carrots and sauce over the rice and spoon a little sauce over the chicken. Green beans, asparagus or a mesclun salad make good accompaniments.