Preheat oven to 350°.
Heat oil in a large nonstick skillet over medium heat. Add mushrooms, onion, and garlic; cook 12 minutes or until mushrooms are tender, stirring occasionally. Stir in raisins, pepper, salt, tomatoes, and spinach. Remove from heat; cool slightly.
Combine milk, 1/2 cup cheese, and eggs in a large bowl, stirring with a whisk. Stir in mushroom mixture. Add bread; stir gently to combine. Let stand 10 minutes. Spoon into a 2-quart baking dish coated with cooking spray. Sprinkle with remaining 1/2 cup cheese. Bake at 350° for 45 minutes or until pudding is set and lightly browned.