In a large mixing bowl, combine the chopped kale, minced garlic, lemon juice, Dijon mustard, honey, extra virgin olive oil, and the second measure of kosher salt. Toss until the kale is well coated and begins to soften.
In a skillet over medium heat, add 1 tablespoon of olive oil. Once hot, add the chopped mushrooms and a pinch of salt. Sauté until tender and golden brown, about 5 to 7 minutes. Remove from heat and let cool slightly.
In a bowl, whisk together the eggs and miso paste (or soy sauce) until well combined. Heat the skillet again and pour in the egg mixture. Cook over low heat, gently stirring with a spatula to create fluffy curds. Once mostly set, add the sautéed mushrooms and half of the grated Pecorino Romano cheese. Fold the omelet in half and cook for an additional minute until fully set.
Place the prepared kale salad onto serving plates. Top each serving with the warm mushroom omelet, then sprinkle with the remaining Pecorino Romano cheese and chopped nuts. Drizzle with chile oil or sauce if desired and finish with freshly ground black pepper.
