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1
Heat oven to 400 degrees.
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2
Put honey in a small saucepan and cook over medium-low heat until lightly golden brown, about 5 minutes.
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3
Add vinegar and cook until reduced and thickened, about 15 minutes.
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4
This sweet deglazed sauce is called a gastrique.
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5
Season to taste with salt and pepper.
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6
Keep warm.
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7
Mix together the butter and blue cheese in a small bowl until well blended, and season to taste with salt and pepper.
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8
Using your fingers, gently loosen the skin from the chicken breasts and stuff about 1 heaping tablespoon of the blue cheese butter under the skin of each breast, smoothing the skin to evenly distribute the butter over the surface of the breast meat.
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9
Season both sides of the chicken with salt and pepper.
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10
Heat oil in large ovenproof saute pan over medium heat until it begins to shimmer.
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11
Put chicken in the pan, skin-side down, and cook until fat renders and skin is golden brown and crispy, about 5 minutes.
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12
Turn chicken and add four rosemary sprigs to pan.
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13
Place in oven and roast until breasts are just cooked through, about 5 minutes longer.
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14
Remove pan from oven and heat broiler.
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15
Spread the remaining butter over the tops of each breast and place under the broiler until golden brown and blistered.
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16
Remove each breast to a plate, spoon some of the pan drippings over each breast and immediately drizzle with some of the gastrique.
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17
Garnish with rosemary.
