Heat oil in a Dutch oven over medium-high. Add onion and carrots, and cook, stirring occasionally, until beginning to soften, about 4 minutes. Add garlic, rice, salt, and pepper, and cook until fragrant and rice begins to toast, about 3 minutes.
Stir in stock, and add Parmesan rind; bring to a boil. Reduce heat to low. Cover and simmer until rice is just cooked through, about 18 minutes. Uncover and discard rind; stir in chicken. Cook until chicken is heated through, about 5 minutes.
Stir in parsley and lemon juice just before serving, and top with shaved Parmesan.