Bring broth to a simmer in a large pot over medium heat. Cook broccoli in simmering broth for 15 minutes.

Meanwhile, in a separate skillet over medium heat, melt margarine. Add onion and sauté for 5 minutes, or to desired tenderness. Stir flour into onion until pasty. Gradually add milk and stir until thick.

Add onion mixture to broccoli mixture in the pot and stir well. Stir in cheese until melted; do not boil. Season with white pepper.