Make the salad dressing by combining the vinaigrette ingredients in a jar with a tight fitting lid (like a mason jar) and shake well to combine. Taste and add more salt as needed.
Whisk the miso paste with the eggs. Heat a frying pan over medium-high heat and swirl in the olive oil. Add in the mushrooms and sauté for 2 minutes, or until mushrooms softened. Add in the egg and turn the heat to medium. Let cook for 2 minutes. Cover and let cook for an additional 1-2 minutes or until eggs are set.
While eggs are cooking, place the kale in a large bowl. Sprinkle with salt. Using massaging motion, rub the kale leaves together to break up and soften the kale.
When ready to serve, slice omelet in strips. Toss kale with some of the dressing (I used about 1/4 cup of the dressing), chopped nuts and Pecorino Romano cheese. Serve with omelet.