Heat olive oil in a large soup pot over medium heat. Add onion, a pinch of salt, and red pepper flakes. Cook for about 3 minutes, until softened.
Add garlic and cook 1 more minute, just until fragrant.
Add the raw chicken directly to the pot. Season lightly with salt and pepper. Cook for 3–4 minutes, stirring, until the outside of the chicken is no longer pink (it will finish cooking in the soup).
Add squash, zucchini, carrots, sun-dried tomatoes, Italian seasoning, and another pinch of salt. Turn heat slightly higher and cook 3–5 minutes, letting the vegetables soften and soak up flavor.
Pour in chicken stock and add the parmesan rind. Bring to a boil.
Add pasta, reduce to a steady simmer, and cook 10–12 minutes, stirring occasionally, until pasta is tender and chicken is fully cooked.
Turn heat to low. Stir in spinach, heavy cream, and pesto. Let spinach wilt and the soup gently thicken.
Remove parmesan rind. Taste and adjust seasoning with salt and pepper.
Serve hot with ricotta, parmesan, a drizzle of olive oil, flaky salt, and cracked pepper.