Prep vegetables: finely dice onion, mince garlic, and chop broccoli into bite size pieces. Set each aside separately.
Heat about 2 tablespoons of oil in a heavy bottomed stock pot or dutch oven over medium heat
Once hot, add onions and cook until soft and fragrant, about 5 minutes.
Add the garlic to the pot and cook for one minute, stirring constantly as to not burn garlic.
Sprinkle flour in the pot, whisking constantly. Cook until onion and garlic are coated and flour starts to smell toasty, about 2-3 minutes.
Slowly whisk in chicken broth, making sure that flour clumps dissolve. Then add in broccoli, bay leaf, and ground mustard.
Bring to a boil, then reduce heat and simmer covered for 10 minutes.
Remove bay leaf before blending.IMMERSION BLENDER*: Using a hand blender, blend your soup until most of your ingredients are blended, leaving as many/as large of broccoli chunks as you prefer.TRADITIONAL BLENDER: Transfer about ½ of your soup to a blender. Carefully** blend your soup until there are no more chunks. Transfer back into the pot with the other ½ of your unblended soup. Mix in heavy cream and cheddar cheese. Stir until cheese is melted and thoroughly combined.
Top with fresh time, croutons, and an additional sprinkle of cheese. Enjoy!