Melt 2 tablespoons of the butter in a deep skillet or Dutch oven over medium heat. Add the garlic and cook for 30 seconds.
Stir in the orzo and cook for 1 minute, stirring, until lightly toasted.
Add the broth and bring to a boil. Reduce the heat and simmer for 8–10 minutes, stirring often, until the orzo is almost tender and most of the liquid is absorbed.
Season the shrimp with the salt and pepper and nestle them into the orzo. Cook for 3–4 minutes, turning once, until pink and opaque.
Stir in the remaining tablespoon of butter and the lemon juice. Top with parsley and Parmesan and serve right away.