This is a terrific summer salad — or side dish — that never fails to garner rave reviews. Ribbons of grilled zucchini, juicy cherry tomatoes and creamy burrata cheese are drizzled with a lively pesto-like arugula sauce, which adds just the right peppery note to pull together and balance the fresh, luscious flavors.
Burrata is a fresh Italian cheese that originated in the Apulia region of Italy. It's a ball of fresh mozzarella with a soft interior of bits of mozzarella and cream, giving it an unusual creamy texture. It's usually served fresh, at room temperature. If you can't find burrata, look for fresh buffalo milk mozzarella cheese instead. You can use yellow summer squash instead of zucchini or a colorful combination of the two, if you like.
Brush each side of the zucchini slices with some of the olive oil and sprinkle each side with salt and pepper. Heat your barbecue or a ridged grill pan over medium heat and cook the zucchini for about 1 minute, then carefully turn the slices and cook another 30 to 45 seconds on the second side. The zucchini should retain its texture, so be careful not to overcook it. Transfer the zucchini to a platter. This is a room-temperature salad, so the zucchini can be prepared several hours in advance.
Place the arugula, parsley, garlic and capers in a food processor and process until the mixture is roughly chopped. With the machine running, add the olive oil and lemon juice in a slow, steady stream, stopping to scrape down the sides of the bowl once or twice. Season the sauce with salt and pepper to taste, and thin with a teaspoon or two of water so that it can be drizzled over the salad.
Scatter the cherry tomatoes, cheese and basil chiffonade over the zucchini. Drizzle the salad with the arugula sauce, then sprinkle the salad with sea salt and pepper, and serve immediately.