In a large mixing bowl, combine the chopped kale, minced garlic, and 1/2 teaspoon kosher salt. Massage the kale gently with your hands for about 2-3 minutes.
In a small bowl, whisk together 1/3 cup lemon juice, 2 tablespoons extra virgin olive oil, 2 teaspoons Dijon mustard, and 2 tablespoons honey until well combined. Season with freshly ground black pepper to taste. Pour this dressing over the kale and toss to coat evenly.
In a skillet, heat 1 tablespoon of olive oil over medium heat. Add the chopped mushrooms and cook until they are golden brown, about 5-7 minutes. Season with a pinch of salt. Set aside.
In a bowl, whisk the 4 eggs with 1 tablespoon of miso paste (or soy sauce) until well combined. Pour the mixture into the same skillet used for the mushrooms.
Once the omelet is partially cooked, add the sautéed mushrooms on one half of the omelet. Sprinkle grated Pecorino Romano cheese over the top. Fold the omelet in half and cook for another minute until the cheese melts and the eggs are fully cooked.
To serve, place a generous serving of the kale salad on a plate, and top it with the warm mushroom omelet. Sprinkle the chopped pecans or walnuts over the salad. Enjoy!