Heat oil in a saucepan over medium heat. Stir in orzo, and cook 1 to 2 minutes, until golden.
Stir in garlic, zucchini, and carrot; cook 2 additional minutes. Add broth; mix well. Bring to a boil. Reduce heat to low and simmer 10 minutes, or until liquid has been absorbed and orzo is tender. Season with thyme (and salt & pepper if desired); top with Parmesan.