Heat 1 tablespoon oil in a large skillet over medium heat. Add chopped onion; cook, stirring often, until softened, 5 to 7 minutes.
Add 8 ounces orzo, the minced garlic, ½ teaspoon mustard, ½ teaspoon paprika, ¼ teaspoon salt and ⅛ teaspoon cayenne; cook, stirring constantly, until toasted and fragrant, about 1 minute.
Stir in cut broccoli and 3 cups broth; bring to a boil over high heat. Reduce heat to maintain a gentle simmer; cook, uncovered and stirring often, until the orzo is tender and most of the liquid has been absorbed, 12 to 15 minutes.
Remove from heat. Stir in 1 cup Cheddar and ¼ cup half-and-half until melted and creamy. Sprinkle with ¼ cup scallions.
