Cut the tomato into quarters, and then grate them on the coarse holes of a box grater. This is a great way to skin and process tomatoes.
Toss the asparagus with 1 Tbsp olive oil and season to taste (salt and pepper will do just fine, but I like to use Cavender's for this). Roast for 10-20 minutes to your desired level of doneness.
While the asparagus broils, whisk the tomato, onion, lemon juice, basil, and olive oil in a small bowl. If you have a stick blender, you can blitz it with that to emulsify the oil and lemon juice. Season to taste with salt and pepper. Place in a small sauce pan to heat up, but don't bring it to a boil.
When the asparagus is done, place it on a serving dish and drizzle with the vinaigrette.