Place the sliced kale in a large mixing bowl. Drizzle with 1 tablespoon olive oil and add a pinch of salt. Massage the kale with olive oil (literally rub the kale handfuls of kale between your fingers) for 3-4 minutes until it turns dark greens and feels very tender. Do NOT skip the massage, people. Tough kale is gross kale. Briefly set aside.
Heat a tablespoon of olive oil in a large saucepan or skillet over medium-high heat. When hot, add the thinly sliced Brussels sprouts and cook for 2-3 minute until bright green and just tender. (Don’t worry if they brown a little bit, that’s a good thing!) Transfer the sprouts to a plate and let cool to room temperature.
Moving on to the dressing! In a small bowl, combine the shallot, lemon juice, maple syrup, and remaining 2 teaspoons olive oil. Season with salt and fresh ground pepper to taste and let stand for 5 minutes.
Add the cooled Brussels sprouts, pomegranate, and avocado to the bowl with the massaged kale. Drizzle with the dressing and gently toss to combine. Transfer to a serving bowl or plate, sprinkle with shaved Parmesan, and serve.