In a large pot, place the chicken broth, broccoli (minus the reserved 1/2 cup) , onions, garlic, carrots an heat until boiling, mixing every minute or so for roughly 7 minutes- until broccoli is nice & tender and onions are soft. set aside.
In a separate large pot, add the butter and flour - on medium heat, whisking constantly.
Remove from heat and pour in your broth/broccoli mixture and slowly, mix well
slowly add in your heavy cream then put on low temp, uncovered and allow to simmer
Next add in all of your spices, the cheeses as well, while stirring consistently.
Simmer about 7 minutes on low-med, mixing occasionally
Place 1/2 cup of reserved broccoli into the microwave and steam until soft.
Garnish your soup with the reserved steamed broccoli and top with grated cheddar.