Preheat oven to 400 degrees.
In a medium sized bowl, toss the shitakes with olive oil and soy sauce. Place in a single layer on a parchment lined baking sheet (for easy clean-up) and roast about 20 to 25 minutes, tossing once. The shitakes should be browned and crispy.
While the mushrooms are roasting, combine the rosemary, orange zest, garlic, Dijon mustard, apple cider vinegar, balsamic vinegar, maple syrup, salt and pepper in the base of your blender. Blend briefly. With the blender on a low speed, slowly but steadily pour in the olive oil. (This can also be done by hand with a whisk.)
In a large bowl, mix the greens, red onion, cranberry and orange segments. When you are ready to serve, add enough dressing to moisten the salad and toss well. Sprinkle the shitakes over the top.