Combine tomatoes, remaining salt + olive oil and basil in a medium mixing bowl. Let sit for at least ten minutes or up to an hour.
Place trimmed asparagus on a baking sheet and drizzle with 2 tbsp olive oil. Sprinkle with 1 tsp salt and pepper. Bake for 10-12 minutes or until cooked through but still crispy. Remove from oven and set aside.
Place asparagus on serving dish. Top with tomato mixture and serve! Optional, drizzle a balsmamic glaze on top!