1.
Trim and slice white mushrooms. Remove and discard shiitake stems; slice caps.
2.
To prepare dressing; combine 4 Tbsp. olive oil, vinegar, mustard, sugar, salt and pepper; set aside.
3.
Just before serving, in a large skillet, over low heat, heat 1 Tbsp. of oil. Add half the mushrooms; cook and stir until golden, about 5 minutes; remove to bowl. Repeat with remaining oil and mushrooms; return cooked mushrooms to skillet; heat until hot.
4.
Stir in reserved dressing. Spoon over salad greens. Garnish with shredded Parmesan cheese, if desired.