Start with the tomatoes. Preheat the oven to 350°F Mix the tomatoes with 3 tbsps of the olive oil and season with some salt and pepper. Spread them out on a baking tray lined with baking parchment, skin side down. Roast in the oven for 40-50 minutes, or until semi-dried. You can leave them there a bit more or a bit less, depending on how dry you like them. They will be delicious anyway. Remove from the oven and leave to cool.
Trim the woody bases of the asparagus and blanch for 4 minutes in plenty of boiling water. Drain and refresh under cold water, making sure the spears are completely cold. Drain well again, then transfer to a mixing bowl and toss with 2 tablespoons of the remaining olive oil and some salt and pepper.
Slice the zucchinis very thinly lengthwise, using a mandolin or a vegetable peeler. Mix with 1 tbsp of the olive oil and some salt and pepper.
Place a ridged griddle pan on a high heat and leave there for a few minutes. It should be very hot. Grill the zucchinis and asparagus, turning them over after about a minute. You want to get nice char marks on all sides. Remove and leave to cool.
Heat the remaining 3 tbsp of olive oil in a pan. Fry the manouri cheese for 3 minutes on each side or until it is golden. Place on kitchen paper to soak up excess oil. Alternatively, chargrill the cheese on the hot griddle pan for about 2 minutes on each side.
To make the basil oil, blitz all the ingredients in a blender until smooth. You might need to double the quantity for some blender blades to be effective. Keep any extra oil for future salads.
To assemble, arrange the rocket, vegetables and cheese in layers on a flat serving plate. Try to build the salad up whilst showing all the individual components. Drizzle with as much basil oil as you like and serve.