Warm the oil in a large skillet over medium-high heat. Add the shallot and the garlic and cook until tender, about 2 mins. Add the mushrooms and cook until golden, about 5 mins.
Add the asparagus and artichokes and cook until the asparagus is tender, about 5 more mins. Turn off the heat and add the tomatoes, salt and pepper and reserve.
For the vinaigrette: Combine the oil, vinegar, tarragon, salt and pepper in a glass screw-top jar.
Seal the jar and shake vigorously to mix the vinaigrette.
Toss the vegetables with the vinaigrette and serve.