Preheat the oven's grill. Place the asparagus on a grill tray and toss with olive oil. Season with salt and pepper to taste. Grill about 5cm from the heat until tender shaking the tin halfway through so that the asparagus cooks evenly. Set aside.
In a bowl combine the asparagus, tomatoes, basil, shallot, oil, garlic, salt and pepper.
Using a slotted spoon, spoon asparagus mixture onto toasted bread. Sprinkle with Stilton.