In a large heavy pot over medium-high heat, melt the butter. Add the chopped onion and a pinch of kosher salt, and cook, stirring occasionally, until the onions are softened and have some browned spots, about 7 minutes. Stir in the chopped garlic and the flour, then continue to cook, stirring constantly, until the garlic is fragrant and the flour is well incorporated, about 1 minute longer.

Pour in the chicken broth and add the broccoli florets along with 1/2 teaspoon kosher salt. Bring the mixture to a boil, scraping up any browned bits from the bottom of the pot. Stir in the gnocchi, reduce the heat to medium, cover, and simmer until the broccoli is just tender, about 5 minutes.

Add the whole milk to the soup and return it to a simmer. Cook, stirring occasionally, until the soup thickens slightly, about 5 minutes. I like to use whole milk for the creamiest texture and best flavor.

Reduce the heat to low and add the Dijon mustard and grated nutmeg. Gradually stir in the shredded cheddar cheese until melted and the soup is smooth, about 3 minutes. Remove the pot from heat, generously season with freshly ground black pepper, and adjust salt to taste.

Ladle the hot soup into bowls. Top with a little extra shredded cheddar and a sprinkle of fresh parsley before serving. For a more vibrant finish, I like to use extra parsley and cheddar as garnish.