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1
Put the chicken in a wide pot.
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2
Add the broth, olive oil, fennel fronds, thyme, garlic, 1 1/2 teaspoons salt and 1/2 teaspoon pepper, then add enough water to cover the chicken and turn the heat to medium low.
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3
Poach the chicken, turning occasionally and keeping the liquid just below a simmer, until just cooked through, about 30 minutes (a thermometer inserted into the center of a chicken breast should register 155 degrees F to 160 degrees F).
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4
Remove the chicken to a plate with a slotted spoon and let cool to room temperature.
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5
Increase the heat to medium high and simmer the cooking liquid until the garlic is tender, about 5 more minutes; remove the garlic and set aside.
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6
Strain the cooking liquid; reserve 1/4 cup and set aside.
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7
While the chicken is cooking, place the red peppers directly on a stovetop gas burner over high heat and char on all sides, turning with tongs, about 10 minutes.
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8
(If you don't have a gas stove, char the peppers on a baking sheet under the broiler, turning occasionally, about 12 minutes.)
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9
Transfer to a bowl, cover with plastic wrap and set aside, 20 minutes.
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10
Peel the skin off the peppers with your fingers; discard the stems and seeds and chop.
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11
Make the aioli: Puree about three-quarters of the roasted red peppers in a blender with the mayonnaise, reserved garlic and 1 tablespoon lemon juice until smooth.
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12
Season with salt and pepper.
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13
Make the salad: Thinly slice the fennel bulbs (use a mandoline if you have one) and transfer to a large bowl.
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14
Finely chop the remaining roasted red peppers, then add to the bowl along with the parsley, the remaining 2 tablespoons lemon juice and the reserved 1/4 cup cooking liquid; toss.
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15
Season with salt and pepper.
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16
Slice the chicken; top with the aioli and serve with the fennel salad.
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17
Photograph by Anna Williams