1. In a large stockpot, melt 1 tablespoon butter over medium heat. Add onion, carrots and garlic; cook for 3 minutes or until vegetables are tender. Add broth, ham hock, peppercorns and thyme; bring to a simmer, and cook, covered, for 30 minutes. Uncover, and continue cooking for 20 minutes.
2. Strain mixture, discarding solids. Pour the liquid into a small saucepan; bring to a simmer over medium-low heat, and cook until reduced by half, about 12 minutes; set aside.
3. Sprinkle fish fillets evenly with salt and peppers.
4. In a large skillet, melt remaining 1 tablespoon butter and olive oil together over medium-high heat. Add fish, and cook for 2 minutes per side or until lightly browned. Add reserved sauce, and simmer for 3 minutes; remove fish from pan, and keep warm. Add green onion to the pan, and continue simmering for 2 minutes longer.
4. Place fish over rice, and spoon sauce over fish. Serve immediately.
Note: If red snapper is not available, substitute tilapia.