In a medium pot, bring the chicken stock and chicken to a simmer. Lower the heat and poach the chicken for 12 minutes.
Heat a dutch oven or soup pot over medium heat. Add the butter to melt. Add the orzo and cook, stirring, until deeply toasted, 3 to 5 minutes. Transfer to a plate.
Add the EVOO, 2 turns of the pan, to the dutch oven. Add the zucchini, carrot, bell pepper, shallots and garlic; season with salt and pepper. Cook, stirring occasionally, until the vegetables are softened, 7 to 8 minutes. Return the orzo to the pot.
Remove the chicken from the stock. Skim and discard the fat from the stock; transfer the stock to the dutch oven. Chop, dice or shred the chicken and add to the soup with 2 cups water. Bring the soup to a boil and cook until the orzo is just tender, 5 minutes. Add the peas during the last minute of cooking. Turn off the heat; stir in the parsley and lemon peel. Serve immediately.