Place flour in small pan; place eggs in small bowl.
Heat half the butter and oil in large nonstick skillet. Coat 3 fillets with flour; dip in eggs. Cook in skillet 2-1/2 minutes per side, until lightly golden. Remove to platter; keep warm. Add remaining butter and oil to skillet. Cook remaining fillets.
To skillet, add leek, carrots, salt and pepper; sauté 4 minutes; if dry, add more butter. Add broth, wine, lemon and capers. Cover; cook 6 minutes, until carrots are tender. Spoon over fish.