Step 1
In a large heavy pot over medium-high heat, melt butter. Add onions and a pinch of salt and cook, stirring occasionally, until softened and browned in spots, about 7 minutes. Add garlic and flour and cook, stirring constantly, until garlic is fragrant, about 1 minute more.
Step 2
Add broth, broccoli, and 1/2 tsp. salt. Bring to a boil, scraping up any browned bits. Stir in gnocchi, reduce heat to medium, and simmer, covered, until broccoli is just tender, about 5 minutes. Add milk, return to a simmer, and cook, stirring occasionally, until cream cheese is melted and soup is thickened, about 5 minutes.
Step 3
Reduce heat to low, add mustard and nutmeg, then gradually stir in cheddar until melted and smooth, about 3 minutes. Remove from heat; generously season with pepper, then season to taste with salt.
Step 4
Divide soup among bowls. Top with more cheddar and parsley.