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