Shred 8 ounces sharp cheddar cheese on the smaller holes of a box grater (about 2 packed cups). Trim the stem end from 1 pound 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 1 large yellow onion (about 2 cups) then add to the bowl with the broccoli stems. Finely grate 6 large garlic cloves (about 4 teaspoons).

Heat 2 tablespoons olive oil in a large Dutch oven or heavy-bottomed pot over medium heat until shimmering, about 30 seconds. Add the onion and broccoli stems, 1 teaspoon of the kosher salt, and ¼ teaspoon of the black pepper. Cook, stirring occasionally, until the onion is translucent and the stems are almost tender, 5 to 7 minutes.

Add the broccoli florets, remaining ¾ teaspoon kosher salt, remaining ¼ teaspoon black pepper, 1 ½ teaspoons ground mustard, and ⅛ teaspoon ground cayenne if desired, and stir to combine. Cook, stirring often, until the florets are vibrant green, 3 to 5 minutes.

Add the garlic and cook, stirring constantly, until fragrant, about 30 seconds. Add 1 pound dried orzo pasta and cook, stirring constantly, until lightly toasted, about 1 minute. Add 1 (32-ounce) carton 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 very 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 (but still glossy), 6 to 8 minutes or according to package instructions. Add 1 cup whole or 2% milk, stir to combine, and simmer until the orzo is al dente but still saucy, about 1 minute more.

Remove the pot from the heat. Add 2 tablespoons unsalted butter and the cheese. Stir until the butter and cheese are melted and the orzo is glossy and saucy. Let sit for 5 minutes for the sauce to thicken before serving.