Trim and roughly chop the zucchini. In a food processor, combine the zucchini, ricotta, flour, a pinch of salt, and some black pepper; blend until a cohesive, slightly sticky dough forms.
Transfer the dough to a pastry bag fitted with a large round tip (or a piping bag). On a well-floured work surface, pipe long strips of dough.
Generously dust the strips with flour, roll them gently to compact, then cut into bite-sized pieces to form the gnocchi.
Bring a large pot of salted water to a boil, then lower to a gentle simmer.
Cook the gnocchi in batches, dropping them into the simmering water. When each batch floats to the surface, remove with a slotted spoon and transfer to a baking dish lightly coated with olive oil to prevent sticking.
Heat a large skillet over high heat. Add the whole cherry tomatoes and let them char and blister until darkened in spots.
Reduce heat to medium, add a drizzle of olive oil and the chopped garlic, and cook briefly until fragrant, about 30 seconds.
Pour in the vinegar to deglaze the pan, then mash the tomatoes with a spoon to create a rustic sauce; simmer briefly to combine flavors.
Add the cooked gnocchi to the skillet, season with salt and pepper, and gently toss to coat, then remove the pan from the heat.
Stir in the chopped basil and grated Parmesan until combined, then serve hot with an extra drizzle of olive oil and a pinch of pepper if desired.
