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.

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.

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.

Preheat oven to 375 degrees F (190 degrees C). Line a rimmed baking sheet with aluminum foil.

Butter both sides of bread with remaining 1 tablespoon butter and place on the lined baking sheet.

Bake bread in the preheated oven, turning halfway through, until toasted and crisp, 4 to 5 minutes.

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.

Set oven rack about 6 inches from the heat source and preheat the oven's broiler.

Place baking sheet under broiler and broil until cheese is browned and bubbly, 3 to 4 minutes.