To make the chimichurri, toss together the shallot, parsley, oregano, garlic, chili, tomato, and red pepper (capsicum) - stir until well mixed. Add in both paprikas, salt, pepper, red wine vinegar, olive oil and water. Stir well. Use immediately or refrigerate to allow flavours to blend. This sauce can me made 3 days ahead – store in the fridge.
Heat your barbecue to high and heat for 10 minutes. Prepare your vegetables by washing and trimming. If you are using root vegetables like sweet potato, beetroot, carrots or sweet potato, prick them with a fork, season with sea salt and black pepper, drizzle with olive oil and wrap them in a few layers of foil. Place the foiled packages directly on barbecue and close the lid – cook on medium for 10-20 minutes, depending upon the size of your vegetables. Turn the package every now and then to prevent burning.
Working in batches, add your softer vegetables (eg, asparagus, peppers, eggplant, zucchini, kale) directly to the barbecue, and let them char. Turn and char on all sides.
To serve, lay our charred vegetables on a large serving board or plate. Add your burrata, a wedge of lemon, and then generously slather over your chimichurri sauce.