Place carrots in the bowl of a food processor, and pulse until carrots are finely chopped.
Add oil and butter to a medium heavy bottomed saucepan, and heat over medium heat. Once oil is hot and butter is melted, add orzo and chopped carrots, and sauté until orzo is golden, about 5 minutes.
Add water, broth, and garlic, and cook uncovered over medium-high heat until all liquid is absorbed, stirring frequently, about 10-15 minutes.
Stir in Parmesan, green onions, rosemary, salt, and pepper. Taste for seasonings. Serve.