Pour the vegetable broth and whole milk into a medium saucepan and bring to a boil over medium-high heat.
Add the finely chopped broccoli, reduce heat to medium-low, and simmer for 2 minutes until the broccoli begins to soften.
Stir in the orzo, sea salt, black pepper, and turmeric (if using). Cook, stirring occasionally, until the orzo is tender, about 8–10 minutes.
Remove the pan from the heat, stir in the grated Parmesan until melted and the sauce is creamy, and taste to adjust seasoning.
Serve immediately.