"This is a meal you can make with less than 10 items, and it could not be easier," Rach says.
Position a rack in the center of the oven and preheat it to 350 °F.
Place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the onions and cook, stirring occasionally, until tender and well caramelized, 35-40 minutes. Remove from heat and cool slightly.
While the onions are caramelizing, fill a large skillet with about an inch of salted water and bring it to a boil. Toss the asparagus into the boiling water and cook about 1 minute until they're bright green and tender. Drain into a colander and run cold water over them to stop them from cooking. Roughly chop them into bite-sized pieces and set them aside.
While the onions are cooling off, whisk together the eggs, milk, mustard, thyme, salt and freshly ground black pepper in a medium-size mixing bowl.
Arrange the bread in the bottom of a 9"x13" baking dish and top with the diced ham, asparagus and caramelized onions, giving everything a light toss to disperse the good stuff throughout the pan. Pour the egg mixture over top of everything.
Sprinkle the shredded cheese over top of the strata and place it on a rimmed baking sheet. Bake it uncovered until puffed and golden brown, and a knife inserted into center comes out clean, about 1 hour. Let stand for 10 minutes then cut the strata into squares and serve.