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1
For the sauce: Heat oil in heavy large pot over medium-high heat. Add lamb riblets and saute until deep brown, turning occasionally, about 18 minutes. Using tongs, transfer the lamb to a bowl.
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2
Add onions, carrots, garlic, and herbs de Provence to pot. Saute until vegetables are deep brown, about 8 minutes.
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3
Add wine and broth to pot; return lamb and any accumulated juices to pot. Bring to boil, reduce heat to medium-low, and simmer uncovered 1 1/2 hours.
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4
Strain into large bowl, pressing on solids in strainer to release all stock. Spoon off any fat from surface of stock; return stock to same large pot. Simmer until reduced to 1 1/3 cups, about 15 minutes.
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5
Mix butter and flour in a small bowl to smooth paste. Whisk paste into stock. Simmer sauce until slightly thickened and smooth, whisking constantly, about 1 minute longer. Season with salt and pepper. (Can be prepared 1 day ahead. Transfer to small saucepan, cover, and chill. Rewarm before using.).
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6
For lamb: Stir fresh herbs and pepper in medium bowl to blend. Add 2 tablespoons oil and mix until herbs are sticking together.
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7
Sprinkle lamb racks with salt. Firmly press 1/3 of herb mixture over rounded side of each rack to cover. (Can be prepared 1 day ahead. Place on large rimmed baking sheet; cover and chill.).
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8
Preheat oven to 350 degrees F. Heat 3 tablespoons oil in large nonstick skillet over medium-high heat. Add 1 lamb rack to skillet, herbed side down and saute until browned, about 4 minutes.
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9
Turn rack over and saute until browned about 3 minutes. Place rack, herbed side up, on rimmed baking sheet. Repeat, fitting remaining racks on same sheet.
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10
Roast lamb until thermometer inserted into center registers 135 degrees F. for medium rare, about 25 minutes. Let lamb rest on sheet 15-20 minutes. Cut lamb between the bones into individual chops.
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11
Arrange 3 chops per plate and drizzle with sauce and serve.
