In a large skillet, cook the salami over medium heat, turning, until just browned, about 3 minutes per batch; drain on paper towels.
In the skillet, heat 1 tablespoon olive oil over medium heat. Add the mushrooms, season with salt and pepper and cook, turning, until tender, about 8 minutes; thinly slice and transfer to a large bowl.
Meanwhile, transfer the breadcrumbs to a plate. In a shallow bowl, beat the eggs. Coat each cheese slice in breadcrumbs, dip in the egg, then coat again with breadcrumbs; place on a sheet of wax paper. In the same skillet, heat 1/4 cup olive oil over medium-high heat. Add 4 cheese slices and cook until crisp, about 1 minute on each side; transfer to a plate. Repeat with the remaining cheese slices.
Add the mixed greens, vinegar, salami and remaining 1 tablespoon olive oil to the mushrooms, season with salt and pepper and toss. Place 2 mozzarella steaks on each of 4 plates and serve with the salad.