Mix the vinegar, sugar, and ¼ teaspoon salt together in a small saucepan. Over high heat, reduce by half. Remove from the heat, drop in the garlic slices, and let the marinade cool. Stir in the olive oil.

Slice the squash in half lengthwise, and scrape out all the seeds. Peel the halves, place cut side down, and cut crosswise, into 1/3-inchthick half-rounds.

Pour vegetable oil into the skillet to the depth of 1/8 inch, and set over medium-high heat. When the oil sizzles on contact with squash, fill the pan with a layer of slices, spaced slightly apart. Fry for about 3 minutes on the first side, then flip the slices over. Fry on the second side another 2 or 3 minutes, until the slices are cooked through (easy to pierce with the tines of a fork), crisped on the surface, and caramelized on the edges.

Lift out the slices with a slotted spoon, draining off oil, and lay them on paper towels. Sprinkle salt lightly on the hot slices. Fry up all the squash in batches, the same way.

Arrange a single layer of fried squash in the bottom of the marinating dish, and scatter 4 or 5 basil leaves on top. Stir up the marinade, and drizzle a couple of spoonfuls over the layer of squash. Scatter some of the garlic slices on the squash too. Layer all the squash in the dish this way, topping each layer with basil leaves, garlic, and marinade. All the seasonings should be used—drizzle any remaining marinade over the top layer of squash.

Wrap the dish in plastic, and marinate the squash for at least 3 hours, preferably overnight in the refrigerator. If chilled, let the squash return to room temperature before serving.