Heat oil in large pot over medium-high heat. Add onions, carrot, garlic, and herbs de Provence to pot. Sauté until vegetables are deep brown, about 8 minutes. 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. Strain into large bowl, pressing on solids in strainer to release all stock. Return stock to same large pot. Simmer until reduced to 1 1/3 cups, about 15 minutes.
Mix butter and flour in 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. DO AHEAD Can be prepared 1 day ahead. Transfer to small saucepan, cover, and chill. Rewarm before using.
Stir fresh herbs and pepper in medium bowl to blend. Add 2 tablespoons oil and mix until herbs are sticking together. Sprinkle lamb racks with salt. Firmly press 1/3 of herb mixture over rounded side of each rack to cover. DO AHEAD Can be prepared 1 day ahead. Place on large rimmed baking sheet. Cover; chill.
Preheat oven to 350°F. Heat 3 tablespoons oil in large nonstick skillet over medium-high heat. Add 1 lamb rack to skillet, herbed side down. Sauté until browned, about 4 minutes. Turn rack over and sauté until browned, about 3 minutes. Place rack, herbed side up, on rimmed baking sheet. Repeat, fitting remaining racks on same sheet.
Roast lamb until thermometer inserted into center registers 135°F for medium-rare, about 25 minutes. Let lamb rest on sheet 15 to 20 minutes. Cut lamb between bones into individual chops. Arrange 3 chops on each plate. Drizzle with sauce and serve.