Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain; drizzle with EVOO.
While the pasta is working, in a small skillet, pour about 2 cups chicken stock over the chicken to cover it. Add the wine and bay leaf; bring to a simmer over medium heat. Make sure the chicken is not sticking to the pan by giving it a wiggle with tongs. Lower the heat to low and gently poach until fully cooked, about 12 minutes.
Meanwhile, in a soup pot, heat 2 tbsp. EVOO over medium-high heat. Stir in the carrots, onion, garlic and thyme; season with salt and pepper. Partially cover and cook until the vegetables are softened, about 10 minutes. Add the remaining stock and the cheese rind, if using; bring to a simmer.
Remove the chicken from the poaching liquid; cut into bite-size cubes and add to the soup. Strain in the poaching liquid. Stir in the peas and parsley; discard the bay leaf.
Spoon the pasta into bowls. Ladle in the hot soup and top with the lemon zest and grated cheese.