Cheddar Strata w/ Grilled Onions

1 teaspoon vegetable oil
2 medium onions, sliced
8 slices rye bread
2 tablespoons Dijon mustard
1 1/2 cups shredded Cheddar cheese (6 ounces)
1 large tomato, seeded and coarsely chopped (1 cup)
1 1/2 cups milk
4 eggs

Heat oven to 300F. Spray square baking dish, 8x8x2 inches, with cooking spray. Heat oil in 10-inch nonstick skillet over medium-high heat. Cook onions in oil 6 to 8 minutes, stirring frequently, until golden brown; remove from heat. Trim crusts from bread. Spread mustard on 1 side of each bread slice. Arrange 4 slices, mustard sides up, in baking dish. Layer 1 cup of the cheese, the tomato and onions on bread. Place remaining bread, mustard sides down, on onions. Beat milk and eggs until well blended. Pour evenly over bread. Bake uncovered about 1 hour or until center is set and bread is golden brown. Sprinkle with remaining 1/2 cup cheese. Let stand 10 minutes before cutting.