Step 1Trim the excess fat from the chicken, season evenly all over with salt (we used a scant 3/4 teaspoon per pound of chicken). Cover loosely and refrigerate. This is best if refrigerated 12 to 24 hours.
Step 2Heat the oven to 375 degrees
Step 3Pat the chicken legs dry; this will make them less likely to stick. Heat the oil in a 12-inch skillet over medium-low heat, then add the chicken legs, skin side down. The oil should sizzle, not pop explosively, when you add the chicken. Adjusting the heat as necessary, cook until the skin is evenly golden, about 8 minutes. Turn the legs over and color only slightly on the other side, about 4 minutes. Pour off the fat.
Step 4If your skillet is ovenproof, arrange the onion wedges in the spaces between the chicken legs; otherwise, transfer the chicken to a shallow flameproof braising dish that will easily hold the chicken and onions in a single layer and add the onions. Add the wine, the vermouth and enough stock to come to a depth of about 1/2 inch. Bring to a simmer and add the bay leaf, thyme and cracked black peppercorns.
Step 5Place, uncovered, in the oven, and cook until the meat is tender but not quite falling off the bone, about 40 minutes. The exposed skin will have turned golden and crisp, the liquid ought to have reduced by about half. Remove from the oven and set on a slight tilt so the fat will collect at one side of the pan.
Step 6Combine the vinegar and honey and warm slightly. This takes 10 seconds in the microwave. The vinegar should dominate but without making you squint. Trim the stems and cut the figs in half.
Step 7Skim as much fat as possible from the braising liquid, then set the pan over medium heat. Bring to a boil and swirl as you reduce the liquid to a syrupy consistency, about 10 minutes. Distribute the figs evenly around the pan, add about 2 tablespoons of the vinegar-honey syrup and swirl the pan to diffuse the bubbling, amber syrup without smashing the tender fruit. The sauce will be glossy. Taste--it should be rich and vibrantly sour-sweet. Add more of the syrup, to taste. The vinegar will fade with boiling, so simmer for only a minute or less.
Step 8Serve each chicken leg with 2 wedges of sweet, soft onion and 4 or 5 figs halves, bathed in a few spoonfuls of the sauce.