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1
Adjust oven rack to upper middle position and preheat oven to 425°F. Place chicken, skin side up, on rimmed baking sheet. Pat dry, then rub with 1 tablespoon oil and season with salt and pepper.
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2
Bake chicken until 3/4 cooked through (about 130°F) and skin is golden, 15 to 20 minutes (Spoon off rendered fat if oven begins to smoke).
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3
While chicken is baking, make glaze. Heat remaining 2 tablespoons oil in medium saucepan over medium heat. Add shallots and 1/4 teaspoon salt. Cook until shallots have softened, about 3 minutes. Add cranberries and 1/2 cup water. Bring to simmer (adjust heat if necessary), and simmer until berries have softened and are breaking down, gently mashing a few times with a potato masher.
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4
Reserve 1/2 cup cranberry mixture. Strain remaining cranberries, pressing firmly against strainer (you should have about 1/2 cup). Return to pot and stir in honey, brown sugar and dry mustard. Bring to simmer over medium high heat and reduce until thick and syrupy, about 3/4 cup. Stir in thyme and season to taste. Reserve about 1/4 cup to glaze chicken.
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5
When chicken is ready, remove from oven and spread 1 tablespoon glaze over each chicken leg. Increase heat to 475°F and cook until chicken is cooked through (170°F) and glaze has darkened and caramelized, 5 to 10 more minutes.
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6
Combine reserved cranberries with remaining glaze (not used to glaze chicken) and serve with chicken.