Shred cheddar cheese on the smaller holes of a box grater (about 2 packed cups). Trim the stem end from broccoli crowns. Cut the florets from the stems. Separate or cut the florets into 1 to 1 ½-inch pieces.

Chop the stems into ¼ to ½-inch pieces and place in a separate medium bowl. Finely chop the yellow onion then add to the bowl with the broccoli stems. Finely grate the garlic.

Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium heat. Add the onion and broccoli stems, 1 teaspoon of kosher salt, and ¼ teaspoon of black pepper. Cook, stirring occasionally, until the onion is translucent and the stems are almost tender.

Add the broccoli florets, remaining kosher salt, black pepper, ground mustard, and ground cayenne if desired, and stir to combine. Cook until the florets are vibrant green.

Add the garlic and cook, stirring constantly, until fragrant. Add dried orzo pasta and cook, stirring constantly, until lightly toasted.

Add low-sodium broth and stir to combine, scraping up the browned bits from the bottom of the pot. Increase the heat to high and bring to a boil.

Reduce the heat to maintain a gentle simmer. Continue to cook, stirring every minute or so and scraping the bottom of the pot, until the orzo is a minute shy of al dente and most of the liquid is absorbed.

Add milk, stir to combine, and simmer until the orzo is al dente but still saucy.

Remove the pot from the heat. Add unsalted butter and the cheese. Stir until melted and the orzo is glossy and saucy. Let sit for 5 minutes before serving.