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1
Trim tops of carrots to 1-inch. Set aside. Tie thyme and sage sprigs together with cooking twine.
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2
Sprinkle chicken evenly with salt and pepper. Place flour in a shallow dish. Dredge chicken in flour. (Alternatively, put flour and salt and pepper in a strong plastic zip bag and one-at-a-time shake chicken leg quarter in bag and press flour onto chicken.) Let chicken pieces rest on a plate (chicken pieces not touching each other) until Step 5.
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3
Melt butter in an 8-quart pressure cooker over medium-high heat.
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4
Add oil to cooker, swirl to coat.
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5
Place 2 chicken leg quarters, flesh side down, in cooker. Saute 5 minutes or until browned. Set aside (fresh plate) until Step 9.
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6
Repeat Step 5 with remaining 2 chicken quarters. When browned, they can be be added to the other chicken leg quarters.
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7
Place mushrooms in cooker. Saute 4 minutes or until liquid evaporates. Remove mushrooms from cooker using a slotted spoon.
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8
Stir in wine, scraping cooker to loosen browned bits. Bring to a boil; cook 30 seconds.
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9
Add chicken, tied herb sprigs, and broth to cooker.
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10
Close lid securely. Bring to high pressure over high heat. Reduce heat to medium or level needed to maintain high pressure. Cook 6 minutes.
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11
Remove cooker from heat. Use quick release method favored by your pressure cooker manufacturer: release pressure through steam vent, or place cooker under cold running water to release pressure.
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12
Remove lid, directing steam away from you.
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13
Transfer chicken to a platter.
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14
Remove vegetables from cooker using a slotted spoon; arrange on the platter with the chicken. Cover and keep warm.
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15
Strain cooking liquid through a cheesecloth-lined sieve into a large bowl. Discard solids.
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16
Transfer liquid to a large, wide skillet over medium-high heat. Bring to a boil. Cook until reduced to 1 cup (about 12 minutes).
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17
Stir chopped thyme and sage into sauce. Serve sauce with chicken and vegetables.