Set a large saucepan over medium heat and add olive oil. When the oil is hot, add the onion. Cook for 3 minutes, stirring frequently until softened. Add the garlic to the sautéed onions and cook for 30 seconds.
Add the rice and orzo. Stir to coat with oil and cook for 2 minutes, until the orzo is lightly golden in color.
Add the vegan chicken broth, lemon juice, and dill. Bring to a boil, then reduce to low heat. Cover and simmer for 20 minutes, or until the rice and orzo are cooked through. Remove from heat. For best results, let the rice and orzo sit, covered, for 10 minutes to firm up.
Gently stir in the parsley and lemon zest. Adjust seasoning to taste and serve hot.