Heat olive oil in a large pot or deep skillet over medium heat. Add garlic and onion, sautéing until fragrant and softened, about 2-3 minutes. Add ground beef, cooking until browned and crumbled, about 5-7 minutes. Season with salt and pepper.
Stir in mushrooms and zucchini, cooking until softened, about 3-4 minutes.
Mix in the orzo, then pour in the broth and vodka sauce. Stir to combine.
Bring the mixture to a gentle boil, then reduce heat to low. Cover and simmer, stirring occasionally, for about 10-12 minutes, or until the orzo is tender and the liquid is mostly absorbed.
Garnish with grated Parmesan cheese and fresh parsley. Serve hot and enjoy!