Boil first 7 ingredients altogether.
Reduce heat, cover, simmer for 15 minutes.
Stir in broccoli and return to boil.
Whisk flour and milk in separate bowl, add to soup.
Stir soup while it thickens, 2-3 minutes.
Remove from heat and let cool.
Process batches of soup in food processor or blender.
Return to heat if necessary.
Top bowls with cheddar cheese as desired.