Grate or roughly chop the zucchini and place in a food processor with the ricotta, flour, a pinch of salt, and some black pepper; process until a smooth, slightly sticky dough forms.
Transfer the dough to a pastry bag fitted with a large round tip (or use a piping bag without a tip). Pipe long strips of dough onto a well-floured work surface.
Dust the strips with additional flour, roll them gently with your hands to seal, then cut into bite-size pieces to form gnocchi.
Bring a large pot of salted water to a boil, then reduce to a gentle simmer.
Cook the gnocchi in batches; when they float to the surface, use a slotted spoon to remove them and place them in a baking dish with a drizzle of olive oil to keep them from sticking.
Heat a large skillet over high heat and add the whole cherry tomatoes; let them char and blister until they darken.
Reduce heat to medium, add a drizzle of olive oil, then add the chopped garlic and cook briefly until fragrant.
Deglaze the pan with the vinegar, then mash the blistered tomatoes with a spoon to create a rustic sauce.
Add the cooked gnocchi to the pan with the sauce, season with salt and pepper, and gently toss to coat. Remove from heat.
Stir in the chopped basil and grated Parmesan, then serve hot with an extra drizzle of olive oil and a pinch of pepper.