Wash and pat dry the vegetables, removing ends and any bad spots.
Line a baking sheet with parchment paper or aluminum foil. Grease with a tablespoon of olive oil.
Add the potatoes, celery, asparagus, and mushrooms in a single line. Drizzle with 1 tablespoon olive oil. Roast in a 425°F oven for 25 minutes, or until the potatoes or soft when pierced with a fork.
Meanwhile, in a small saucepan bring 2 cups of water and a teaspoon of salt to a boil. Add the green beans and boil for 3 - 5 minutes, or until tender but crisp.
Drain the green beans and plunge in ice water. Drain and dry well.
Toss the vegetables and lettuce together in a large salad bowl. Add the feta cheese and sprinkle with chopped walnuts. Serve with Greek Vinaigrette on the side.