In a large nonstick skillet heat oil over medium-high heat. Add asparagus, mushrooms, and sweet pepper; cook about 3 minutes or just until vegetables are crisp-tender.
Lightly coat six 12-ounce individual casserole dishes with cooking spray. Divide half of the English muffin pieces among the dishes. Top with the chicken, asparagus mixture, and 1/2 cup of the cheese. Top with the remaining English muffin pieces.
In a medium bowl whisk together eggs, milk, and black pepper. Pour egg mixture evenly over the layers in dishes. Using the back of a large spoon, press muffin pieces down to moisten. Sprinkle with the remaining 1/4 cup cheese. Cover; chill for 2 to 24 hours.
Preheat oven to 325 degrees F. Bake, uncovered, for 25 to 30 minutes or until a knife inserted in centers comes out clean. Let stand for 10 minutes before serving.