Place the zucchini flesh in a container for an immersion blender. Blend until creamy. Add the zucchini peels, a handful of basil and mint leaves, a drizzle of olive oil, and blend until smooth and creamy. It should be fluid (add a little water if needed). Taste and adjust salt. Transfer to a cup and cover with plastic wrap.

Clean the calamari by removing the outer skin. Separate the tentacles and remove the eyes and beak. Slice the calamari lengthwise and remove any inedible parts. Rinse well, pat dry, and cut into strips lengthwise (don't worry—they'll shrink and curl up). Season with olive oil, a pinch of salt and pepper, and add sprigs of rosemary, oregano, and thyme. Massage well and set aside.

Heat a skillet, and when hot, add the calamari with the herbs, without any added fat. Deglaze with vodka and sauté for no more than 2 minutes (the longer they cook, the tougher they get). Transfer to a plate and cover with plastic wrap (this keeps them moist and tender until cooled). Pour the released liquid back into the skillet for later use.

Wash the Piccadilly tomatoes well. Remove the stem end, then cut them into quarters lengthwise. Remove the seeds, then slice lengthwise again and cut into medium pieces. Place in a container with a pinch of salt and tilt the container so excess water drains off (discard this water). Add the Taggiasca olives and dress with a drizzle of olive oil and fresh oregano leaves.

Cook the pasta in plenty of salted water. A couple of minutes before it's done, transfer it to the skillet with the calamari juices. Toss to flavor, then continue cooking like risotto, adding a little pasta water at a time.

One minute before the pasta is done, add the zucchini cream and continue cooking, adding water as needed until the pasta is cooked (don't let it dry out, as the sauce tends to thicken). At the end, add the calamari and toss everything together.