Preheat oven to 425.
In a large baking dish, toss the red potatoes and tomatoes with the olive oil, balsamic vinegar, dried thyme (if you are using) and salt. Cover with aluminum foil and bake for 20 minutes.
Add asparagus. Bake for another 10-15 minutes, or until potatoes are tender.
Increase oven temperature to 450 degrees. Remove foil, and continue cooking 5 to 10 minutes, until potatoes are lightly browned.
Top with balsamic vinegar, fresh thyme, salt, pepper, and feta cheese.