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1
Cook onions in oil in a 12-inch heavy nonstick skillet over moderately low heat, stirring frequently, until deep golden brown, 25 to 30 minutes.
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2
Transfer to a medium bowl, reserving 3 1/2 tablespoons onions in a small bowl for stuffing and sauce.
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3
(Do not clean skillet.)
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4
While onions are browning, simmer lentils in 1 cup broth and 1 cup water in a 3-quart saucepan, uncovered, stirring occasionally, until just tender, 20 to 25 minutes.
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5
Drain lentils in a sieve, then stir into onions in medium bowl along with salt and pepper.
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6
Cool to room temperature.
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7
Stir together dill, 3 tablespoons parsley, 2 tablespoons reserved onions, and salt and pepper to taste in a small bowl.
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8
Pat chicken dry and cut a 3- to 4-inch-long pocket horizontally in thicker side of each chicken breast.
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9
Gently stuff chicken breasts with herbed onions, then season chicken with salt and pepper.
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10
Prepare grill for cooking.
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11
If using a charcoal grill, open vents on bottom of grill, then light charcoal.
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12
Charcoal fire is medium-hot when you can hold your hand 5 inches above rack for 3 to 4 seconds.
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13
If using a gas grill, preheat burners on high, covered, 10 minutes, then turn off burner directly below where chicken will go and reduce remaining burner(s) to moderately high.
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14
Grill chicken, covered only if using a gas grill, on lightly oiled grill rack, turning over once, until cooked through, 8 to 11 minutes total.
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15
Transfer to a plate and let stand, loosely covered, while making sauce.
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16
Stir together arrowroot and 2 tablespoons broth in a small bowl.
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17
Puree remaining 1 1/2 tablespoons reserved onions with remaining 1 1/4 cups broth in a blender until smooth, then pour into skillet and deglaze by boiling over moderate heat, stirring and scraping up brown bits, 1 minute.
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18
Reduce heat to low, then add arrowroot mixture and cook, stirring, until just thickened, about 1 minute (do not let boil).
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19
Stir in 1/2 teaspoon lemon juice and season with salt and pepper.
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20
Remove from heat and keep warm, covered.
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21
Stir mint, remaining tablespoon parsley, and remaining 2 teaspoons lemon juice into lentils, then toss with lettuce and season with salt and pepper.
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22
Slice chicken, then divide salad among 6 plates and top with chicken, feta, and sauce.
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23
*Available at specialty foods shops and some supermarkets.
