Shred the cheddar cheese using the smaller holes of a box grater.

Trim the stem end from the broccoli crowns, cut the florets from the stems and chop the stems into small pieces.

Finely chop the yellow onion and place it in a bowl with the chopped broccoli stems.

Finely grate the garlic cloves.

Heat olive oil in a large Dutch oven over medium heat until shimmering.

Add the onion and broccoli stems along with 1 teaspoon of kosher salt and 1/4 teaspoon of black pepper. Cook until the onion is translucent and stems tender, about 5 to 7 minutes.

Stir in the broccoli florets, remaining salt, black pepper, ground mustard, and cayenne if desired. Cook until florets are vibrant green, about 3 to 5 minutes.

Add garlic and cook until fragrant, about 30 seconds.

Add the orzo pasta and cook until lightly toasted, about 1 minute.

Pour in the broth and stir to combine, scraping any browned bits from the bottom.

Raise heat to high and bring to a boil, then reduce heat to maintain a simmer. Cook until orzo is nearly al dente, about 6 to 8 minutes.

Add milk and simmer until orzo is al dente and sauce is creamy, about 1 minute more.

Remove from heat and stir in butter and cheese until melted and glossy.

Let sit for 5 minutes to thicken before serving.