1. Preheat the oven to 450 degrees. In a food processor, pulse the English muffin into large, fluffy crumbs. Transfer bread crumbs to a medium bowl; toss with the Parmesan and 2 teaspoons of the oil. Season with the salt and black pepper to taste.
2. Whisk together remaining oil and the shallot, vinegar, soy sauce and thyme and a pinch of black pepper in a small bowl.
3. Spread the asparagus evenly on two rimmed baking sheets. Drizzle each sheet with 2 tablespoons of the dressing; shake to coat.
4. In another medium bowl, toss the mushrooms with 2 tablespoons dressing. Scatter mushrooms evenly over asparagus, reserving bowl. Roast the vegetables 10 minutes.
5. Toss roasted asparagus and mushrooms to coat with their cooking juices and scatter bread crumbs over each sheet. Return sheets to oven and roast another 8 to 10 minutes or until vegetables are tender and bread crumbs are browned.
6. In reserved bowl, toss the salad greens with 2 tablespoons dressing; store leftover dressing in the refrigerator. Pile the salad on dinner plates. Top with asparagus and mushrooms, sprinkle with the chopped egg and serve.