In a medium pan, melt butter over medium-high heat. Add onion and cook for 5 minutes until yellow. Add flour and stir.
Add chicken broth and cook, stirring constantly, until mixture is slightly thickened. Add milk and leave to boil, stirring constantly.
Pour mixture into blender. Cover and blend at medium speed for 30 seconds until smooth. Put it back in the pan and heat until just boiling.
Remove from heat, add cheese and stir with a slotted spoon until cheese melts. If cheese doesn't melt completely, put over very low heat for about 1 minute, stirring constantly. You can add salt and white pepper if you want. Serve immediately.
