Blanch the asparagus in boiling, salted water for 1-2 minutes. Drain, then rinse in cold water and pat dry. Divide the asparagus between 4 plates or arrange on a platter.
In a small bowl mix the tomatoes, shallots, garlic, olive oil and lemon juice and some seasoning, until combined. To serve, pour the tomato mixture over the asparagus and top with the crumbled cheese and basil.