Preheat oven to 400°F (200°C). Slice off the top of the garlic head to expose cloves, drizzle with olive oil, wrap in foil, and roast for 30-35 minutes until soft and golden. Cool and squeeze cloves out of skins.
In a medium saucepan, bring vegetable broth to a gentle boil. Add orzo and cook for 8-10 minutes until tender but slightly firm. Drain excess broth, reserving some for thinning sauce.
Return cooked orzo to saucepan over low heat. Stir in heavy cream and roasted garlic cloves, mashing garlic to distribute. Cook 2-3 minutes to meld flavors.
Gradually mix in grated Parmesan cheese, stirring constantly until melted and sauce thickens. Season with salt and freshly ground black pepper. Add reserved broth if sauce is too thick.
Transfer orzo to serving bowls and garnish generously with chopped fresh parsley. Serve warm.
