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1
One at a time, place each chicken breast between pieces of plastic wrap or parchment and lightly pound with a mallet until it is 1/2 to 3/4 inch thick.
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2
Chicken breasts should be of uniform thickness.
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3
Place chicken breasts in a bowl, season with salt and pepper and toss with rosemary, garlic and 2 tablespoons olive oil.
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4
Cover bowl and refrigerate for 30 minutes to an hour.
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5
Place oven on lowest setting, around 200 degrees.
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6
Cook the chicken: Heat a large cast-iron skillet or grill pan over high heat for 5 minutes.
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7
Add remaining olive oil to pan and reduce heat to medium-high.
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8
Turn over chicken breasts in marinade to coat them, then add them to the pan, rounded side down.
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9
Cook for 4 to 5 minutes on one side, until cooked halfway through.
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10
Turn chicken breasts over and carefully arrange feta on top, dividing it equally among the 4 breasts.
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11
Sprinkle about 1/4 teaspoon thyme leaves over feta on each breast.
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12
Cook 4 to 5 minutes, until breasts are cooked through.
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13
Feta will warm but will not melt.
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14
Transfer to a baking sheet and keep in warm oven while you cook the figs.
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15
Add wine to pan and scrape with a wooden spoon to deglaze the bottom.
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16
Boil wine until it has reduced by half, then add figs, honey and remaining thyme.
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17
Cook, stirring, until figs break down and begin to look jammy, about 3 minutes.
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18
Remove from heat.
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19
Serve chicken breasts with fig compote on side and garnish with rosemary sprigs.
