Begin by shredding 8 ounces of sharp cheddar cheese into approximately 2 packed cups using the smaller holes of a box grater. Separate the broccoli crowns into florets (1 to 1 1/2-inch pieces) and dice the stems into 1/4 to 1/2-inch pieces. Finely dice the onion and mince the garlic cloves.

In a large Dutch oven or heavy-bottomed pot, heat 2 tablespoons of olive oil over medium heat until shimmering. Add the diced onion, broccoli stems, 1 teaspoon kosher salt, and 1/4 teaspoon black pepper. Cook for 5-7 minutes, stirring occasionally, until the onions become translucent and the broccoli stems begin to soften.

Incorporate the broccoli florets into the pot along with the remaining 3/4 teaspoon kosher salt, 1/4 teaspoon black pepper, dry ground mustard, and optional cayenne pepper. Stir well and cook for an additional 3-5 minutes until the florets turn a vibrant green.

Stir in the minced garlic, allowing it to cook for 30 seconds until fragrant. Add the dried orzo pasta, stirring continuously for 1 minute to lightly toast the pasta.

Pour the broth into the pot, scraping up any browned bits from the bottom. Increase the heat to high and bring the mixture to a boil. Once boiling, reduce the heat to maintain a gentle simmer. Cook for 6-8 minutes, stirring frequently to prevent sticking, until the orzo is nearly al dente and most of the liquid has been absorbed.

Stir in 1 cup of milk and continue to simmer for 1 minute until the orzo reaches an al dente texture and the mixture remains saucy. Remove the pot from heat, then incorporate 2 tablespoons of butter and the shredded cheddar cheese. Stir until the cheese and butter have melted, creating a glossy, creamy sauce.

Let the dish rest for 5 minutes to thicken slightly. Serve warm for the best flavor and texture.