Heat oil in 12-inch nonstick skillet over medium heat until hot. Add onion, bell pepper and garlic; cook 6 to 8 minutes or until tender, stirring frequently. Stir in ham. Add tomatoes; cook an additional 2 minutes.
Spray 13x9-inch (3-quart) glass baking dish with nonstick cooking spray. Place torn bread in sprayed baking dish. Top with ham mixture.
In large bowl, combine eggs, milk, salt and pepper; beat well. Pour over mixture in baking dish. Cover; refrigerate at least 6 hours or overnight.
Heat oven to 350°F. Uncover strata; bake 30 minutes. Sprinkle with cheese; bake an additional 30 minutes or until knife inserted in center comes out clean.