In a medium saucepan, combine 2 cups vegetable broth and 1 cup whole milk and bring to a gentle boil over medium heat.
Add 1 cup orzo to the boiling liquid, reduce heat to maintain a gentle simmer, and cook for 8–10 minutes, stirring occasionally to prevent sticking, until the orzo is tender.
Lower the heat to medium-low and stir in 1 cup grated Parmesan and 4 oz roughly chopped baby spinach until the cheese melts and the spinach wilts, about 2–3 minutes.
Taste and season with 1/2 tsp salt and 1/2 tsp black pepper, adjusting to preference, then serve warm.