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1
Adjust oven rack to middle position and heat oven to 400u00b0F.
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2
Brine the chicken: Dissolve 1/4 cup salt in 2 quarts cold tap water in large container or bowl. Submerge chicken pieces in brine and refrigerate until fully seasoned, about 30 minutes. Rinse chicken pieces under running water and thoroughly pat dry with paper towels. Season both sides of chicken pieces with pepper.
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3
Meanwhile, toss garlic and shallots with 2 teaspoons olive oil and salt and pepper to taste in 9 inch pie plate; cover tightly with foil and roast until garlic is softened and beginning to brown, about 30 minutes. Shake pan once to toss the contents after 15 minutes (foil can be left on during tossing). Uncover, stir, and continue to roast, until browned and fully tender, about 10 minutes longer, stirring once or twice. Remove from oven and increase oven temperature to 450u00b0F.
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4
Using kitchen twine, tie together thyme, rosemary, and bay leaf and set aside.
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5
Heat remaining 1 teaspoon oil in 12-inch heavy-bottomed ovenproof skillet over medium-high heat until it begins to smoke. Swirl to coat pan with oil. Brown chicken pieces skin-side down until deep golden, about 5 minutes. Turn chicken pieces and brown until golden on second side, about 4 minutes longer.
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6
Transfer chicken to large plate and discard fat. Off the heat add vermouth, chicken broth, and herbs, scraping bottom of skillet with wooden spoon to loosen browned bits.
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7
Set skillet over medium heat, add garlic and shallot mixture to pan, then return chicken, skin-side up to the pan, nestling pieces on top of and between the garlic cloves.
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8
Place skillet in oven and roast until instant-read thermometer inserted into thickest part of breast registers about 160 F about 10 to 12 minutes. If desired, increase heat to broil and broil to crisp skin about 3 to 5 minutes.
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9
Using potholders or oven mitts, remove skillet from oven and transfer the chicken to a serving dish. Set the skillet aside on the stovetop, reserving the liquid.
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10
Remove 10 to 12 garlic cloves and place in a mesh sieve and set aside. Using a slotted spoon, scatter the remaining garlic cloves and shallots around the chicken and the discard herbs.
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11
With a rubber spatula push reserved garlic cloves through the sieve and into a bowl. Discard the skins.
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12
Add the garlic paste to the remaining liquid in the skillet. Bring to a simmer over medium high heat, whisking occasionally to incorporate the garlic. Adjust seasoning with salt and pepper to taste. Whisk in butter. Pour sauce into sauceboat and serve with the chicken.
