In a large pot over medium heat, bring the chicken broth to a simmer. Cook the broccoli in the simmering broth for 15 minutes.
In a separate skillet over medium heat, melt the margarine. Add the chopped onion and sauté for 5 minutes or until it reaches your desired tenderness.
Mix the flour into the onion until it forms a paste. Gradually add the milk, stirring continuously until the mixture thickens.
Combine the onion mixture with the broccoli mixture in the pot, stirring well.
Stir in the cheese until it is melted, making sure not to boil the mixture.
Season with ground white pepper before serving.