Heat oil in a large nonstick skillet over medium-high heat. Add onion, thyme, and garlic; sauté 3 minutes or until tender. Spoon onion mixture into a bowl; set aside. Add mushrooms to skillet. Cover and cook over low heat 8 minutes or until liquid nearly evaporates, stirring occasionally. Set aside.
Combine water and salt in a large saucepan; bring to a boil. Gradually add cornmeal; stir constantly with a whisk. Cook 2 minutes; stir constantly. Remove from heat; stir in onion mixture, mushrooms, milk, and egg yolks.
Beat egg whites at high speed of a mixer until stiff peaks form. Gently fold egg whites into cornmeal mixture. Pour into a 2-quart soufflé dish coated with cooking spray. Bake at 400° for 40 minutes or until puffy and set.