Combine chicken broth and lemon juice in small saucepan; simmer until reduced by half, about 5 minutes. Stir in butter, cornstarch, and capers. Heat through; cover and keep warm.
Sauté carrots and onions in heavy nonstick skillet in 1 tablespoon oil until tender, about 5 minutes. Remove from pan and keep warm.
Rinse any ice glaze from frozen Alaska Sole fillets under cold water; pat dry with paper towel. Brush both sides of fillets with remaining oil. Place fillets in pan and cook, uncovered, over medium-high heat about 3 minutes, until browned. Shake pan occasionally to keep fish from sticking.
Turn fillets over and season with salt and pepper. Cover pan tightly and reduce heat to medium. Cook an additional 2 to 5 minutes. Cook just until fish is opaque throughout.
Serve each fillet with 1/2 cup vegetables and 2 to 3 tablespoons sauce. Garnish with fresh dill, if desired.
Tip: This recipe is also excellent with Alaska Cod or Alaska Pollock.