Preheat oven to 400 degrees F
Season thighs generously with salt and pepper and lightly dredge in flour.
Melt the butter in a large, heavy-bottomed pot or skillet set over medium-high heat. When the butter foams, cook the chicken skin-side down until a golden brown crust forms, around 8-10 minutes. Flip and sear the other side until light brown, 3-5 minutes. Do this in batches if necessary. Remove to a plate and set aside.
If there is a lot of fat in the pan, remove all but 1 tablespoon. Turn down the heat to medium, add the shallots and sauté them until they begin to soften and caramelize, approximately 5-7 minutes. Add the garlic and sauté for 30 seconds, until softened but not brown. Add the wine and simmer until reduced by about half, scraping up any brown bits that might have stuck to the bottom of the pan, 3 to 5 minutes, then add the stock, mustard and thyme and stir to combine and bring to a boil. Add back the chicken, skin-side up.
Place into oven and roast until completely cooked through, reaching an internal temperature of 175 degrees F, about 25-30 minutes. (if using boneless thighs or breasts, start checking after 20 minutes).
Add the lemon juice and cherry tomatoes to the pot, stir lightly to combine and serve immediately.