In a large skillet over medium heat, melt butter. Add onion; season with salt and pepper. Cook, stirring occasionally, until softened, about 7 minutes.
Add broccoli and cook, stirring, until florets are crisp and bright green, 3 to 5 minutes. Add garlic and cook, stirring, until fragrant, about 1 minute more. Add orzo and cook, stirring constantly, until starting to look toasty, about 1 minute.
Stir in broth; season with salt. Increase heat to high and bring to a boil, scraping any browned bits on bottom of pot. Reduce heat to medium-low and simmer, stirring frequently, until most of the liquid is absorbed, about 7 minutes. Stir in milk, return to a simmer, and cook, stirring frequently, until creamy and orzo is cooked through, about 1 minute more.
Remove from heat and stir in cheddar. Let sit until cheese is melted and thickened, about 5 minutes. Stir again to combine, then top with chives.
