Whisk eggs, milk and pepper in large bowl until blended. Reserve 1/2 cup cheese. Add remaining cheese to egg mixture with all remaining ingredients; mix well.
Cut 3 (30-inch-long) sheets of foil. Fold 1 sheet lengthwise in half twice; repeat with second sheet. Fold remaining sheet to fit inside back edge of slow cooker; place in slow cooker. Crisscross foil strips; use to line bottom and sides of slow cooker. Spray inside of slow cooker with cooking spray. Add egg mixture. If necessary, press toast cubes into egg mixture with back of spoon to completely moisten toast cubes.
Cook on LOW 4 hours, sprinkling with reserved cheese for the last 15 min. Cool slightly. Use foil handles to transfer strata from slow cooker to platter; discard foil.