Step 1
Melt 1 tablespoon butter in a large pot over medium heat; add onion. Cook and stir until onion turns translucent 5 to 6 minutes. Add garlic; stir for 1 minute. Pour in broth; bring to a simmer over high heat.
Step 2
Separate florets from heads of broccoli. Cut large florets in half. Cut stems in half and cut into 1/2-inch pieces. Add broccoli to simmering broth. Cover and cook until broccoli softens slightly 2 to 3 minutes. Reduce heat to medium-low; simmer stirring occasionally until broccoli is very tender about 10 minutes. Remove from heat.
Step 3
Blend broccoli with an immersion blender into a very smooth puree. Stir in cream salt pepper nutmeg and cayenne. Return soup to medium-low heat; cook until cream is heated through about 5 minutes.
Step 4
Preheat oven to 375 degrees F (190 degrees C). Line a rimmed baking sheet with aluminum foil.
Step 5
Butter both sides of bread with remaining 1 tablespoon butter and place on the lined baking sheet.
Step 6
Bake bread in the preheated oven turning halfway through until toasted and crisp 4 to 5 minutes.
Step 7
Place 6 oven-proof soup crocks on the foil-lined baking sheet. Ladle soup into the crocks filling almost to the top. Place 1 piece of toasted bread in each crock; cover with Cheddar cheese.
Step 8
Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
Step 9
Place baking sheet under broiler and broil until cheese is browned and bubbly 3 to 4 minutes.