In a medium saucepan, combine the vegetable broth, whole milk, and the finely chopped broccoli and bring to a boil over medium-high heat.
Reduce heat to medium-low and simmer the mixture for 2 minutes to soften the broccoli.
Add the orzo, sea salt, pepper, and turmeric (if using), then cook, stirring occasionally, for 8–10 minutes until the orzo is tender and most of the liquid is absorbed.
Stir in the grated Parmesan and cook for about 1 more minute until the cheese is melted and the sauce is creamy.
Remove from heat, taste and adjust seasoning if needed, then serve immediately.