Utilize the smaller holes of a box grater to shred 8 ounces of sharp cheddar cheese into approximately 2 packed cups. Remove the stem end from 1 pound of broccoli crowns. Detach the florets from the stems and divide them into 1 to 1 1/2-inch pieces.

Dice the stems into 1/4 to 1/2-inch pieces and place them in a medium bowl.

Finely chop 1 large yellow onion until you have about 2 cups and add it to the bowl containing the broccoli stems. Mince 6 large garlic cloves to yield about 4 teaspoons.

Heat 2 tablespoons of olive oil in a large Dutch oven or heavy-bottomed pot over medium heat until it begins to shimmer. Add the chopped onion and broccoli stems, 1 teaspoon of the kosher salt, and 1/4 teaspoon of the black pepper. Stir occasionally and cook until the onion becomes translucent and the stems nearly tender, approximately 5 to 7 minutes.

Introduce the broccoli florets to the pot along with the remaining 3/4 teaspoon kosher salt, the remaining 1/4 teaspoon black pepper, 1 1/2 teaspoons ground mustard, and 1/8 teaspoon ground cayenne if using. Stir well and cook until the florets turn vibrant green, which should take about 3 to 5 minutes.

Add the minced garlic to the pot and stir constantly for about 30 seconds until fragrant. Then add 1 pound of dried orzo pasta and continue to stir constantly, allowing the orzo to toast slightly for about 1 minute.

Pour in one 32-ounce carton of low-sodium broth and stir to combine while scraping up any browned bits from the bottom of the pot. Increase the heat to high and bring the mixture to a boil.

Once boiling, reduce the heat to maintain a gentle simmer. Continue cooking, stirring every minute and scraping the pot's bottom, until the orzo is almost al dente and most of the liquid has been absorbed but is still glossy, which should take about 6 to 8 minutes, or according to the package instructions.

Add 1 cup of whole or 2% milk, stir to combine, and continue to simmer until the orzo is al dente but still saucy, about 1 minute more.

Remove the pot from heat, incorporate 2 tablespoons of unsalted butter and the shredded cheese, stirring until both are completely melted and the orzo appears glossy and saucy.

Allow the dish to sit for 5 minutes after cooking to let the sauce thicken. Serve warm for the best flavor and texture.