Cut each bread slice diagonally into 4 triangles. Arrange half of the bread triangles in ungreased rectangular pan, 13 x 9 x 2 inches. Top with vegetables. Sprinkle with cheese. Top with remaining bread.
In a medium-size bowl, beat remaining ingredients with hand beater or wire whisk until well mixed. Pour evenly over bread. Cover and refrigerate at least 2 hours but no longer than 24 hours.
Heat oven to 325 degrees F. Cover and bake 30 minutes. Uncover and bake an additional 45 minutes (or until knife inserted in center comes out clean). Let stand 10 minutes before cutting.