Halve each tomato horizontally and put them, cut side up, on a baking sheet. Drizzle ½ teaspoon olive oil over each, season with salt and pepper, half a crushed garlic clove and a sprig of thyme. Cook in a preheated oven, 110°C (225°F), Gas Mark ¼, for at least 2 hours. The tomatoes should be slightly dehydrated but still juicy.
Whiz the wild garlic, basil and 5 tablespoons olive oil in a food processor. The garlic should still be slightly chunky. Place in a bowl and whisk in the vinegar. Season with salt and pepper.
Arrange the asparagus on a dish and drizzle over ½ tablespoon oil. Season with a little salt and pepper. Heat a griddle pan over a high heat and cook the asparagus for about 5 minutes, turning the spears every 1—2 minutes. They will be just tender in the middle. Return the asparagus to the dish, cover with clingfilm and leave to steam slightly.
Remove the tomatoes from the oven and arrange on serving plates. Top each tomato with 5 asparagus spears and a drizzle of the wild garlic dressing. Serve with the rocket and a sprinkling of Parmesan cheese.