In a large pot over medium heat, add the olive oil, onion, fennel, garlic, salt, and pepper. Cook partially covered, stirring every few minutes, until the onion is soft and translucent, about 5 minutes.
Add the zucchini, reduce the heat to medium-low, and continue cooking, covered, for 15 minutes, stirring every 5 minutes to prevent sticking.
Pour in the chicken stock and add the fresh basil. Increase the heat to medium and bring the soup to a gentle simmer. Cook for 15 minutes, or until the zucchini and fennel are completely tender.
Remove the pot from the heat. Using an immersion blender or blender, carefully blend the soup until silky smooth and creamy. Taste and adjust the seasoning with additional salt and pepper if needed.
Ladle into bowls and garnish with parmesan crisps and thinly sliced jalapeños before serving.