Place porcini mushrooms and tomatoes in separate small bowls. Cover both mushrooms and tomatoes with boiling water; soak for 15 minutes. Drain well. Rinse mushrooms. Drain again, pressing out excess moisture. Chop dried tomatoes; set aside.
In a 2-quart square baking dish, toss together English muffin or bread pieces, mushrooms, tomatoes, corn, cheese, basil, salt, and pepper. In a medium bowl, combine eggs and milk; beat with a wire whisk or rotary beater until well mixed. Pour egg mixture evenly over mixture in baking dish. Cover and refrigerate for at least 4 hours or up to 24 hours.
Preheat oven to 375F. Bake, uncovered, about 45 minutes or until a knife inserted in center comes out clean. Let stand for 10 minutes before serving. Makes 6 side-dish servings.