Heat the oil in a large, heavy-based pot over medium heat. Add the leek and cook, stirring occasionally, for 2 to 3 minutes or until the leek begins to soften. Add the zucchini and tomatoes and cook, stirring occasionally, for 5 minutes.
Add the chickpeas, the stock and the parmesan rind (or the parmesan chunk if a rind isn’t available) and bring to a boil.
In a separate pot, bring water to a rapid boil and cook the pasta for 1 minute less than the packet directions say (see notes). Drain and refresh in cold, running water. Set aside.
Meanwhile, to make the pistou, crush the garlic cloves and sea salt into a paste using a mortar and pestle. Add the torn basil leaves and pound everything together until mostly smooth. Stir in the olive oil to make it saucier and set aside until the soup is ready.
Once the broth comes to a boil, reduce the heat to low and stir in the asparagus, baby spinach and extra grated parmesan. Simmer for 3 minutes or until the baby spinach starts to wilt.
Remove from the heat, add in the cooked pasta, lemon zest and juice, and stir. Taste and season with a little salt, if needed.
Ladle the minestrone into bowls, top each with a teaspoon of pistou, extra parmesan and serve with chunks of focaccia (optional).