Place all the ingredients in a blender and process until smooth.
Toss the cherry tomatoes with 3 tablespoons of olive oil. Spread them onto a parchment lined baking sheet and place in a preheated MEDIUM-LOW 325°F (163°C) grill for 50 minutes, until semi-dried. Toss the zucchini and asparagus with 2-3 tablespoons olive oil. Grill until just tender and crisp. Let cool on a rack. Heat the remaining 3 tablespoons olive oil in a skillet. Fry the Manouri cheese for 3 minutes per side, until golden, cube. Drain on a paper-towel lined plate.
Arrange the vegetables and cheese on a large platter and drizzle with some basil oil, to taste. Reserve remaining dressing for another time.