In a large saucepan, bring 8 cups water to a boil. Add asparagus; cook, uncovered, 2-3 minutes or just until crisp-tender. Drain and immediately drop into ice water. Drain and pat dry.
Arrange six English muffin halves in a greased 13×9-in. baking dish, cut side up. Trim remaining muffin halves to fill spaces. Layer with 1 cup cheese, asparagus, ham and red pepper.
In a large bowl, whisk eggs, milk, salt, mustard and pepper. Pour over top. Refrigerate, covered, overnight.
Preheat oven to 375°. Remove strata from refrigerator while oven heats. Sprinkle with remaining cheese. Bake, uncovered, 40-45 minutes or until a knife inserted in the center comes out clean. Let stand 5 minutes before cutting.