Whisk together yogurt, cheese, lime juice, olive oil, Worcestershire sauce, garlic, mustard, sea salt, and pepper. Add almond milk 1 tablespoon at a time, until the desired dressing consistency is reached. Set dressing aside.
Combine kale, romaine lettuce, chicken breast, cherry tomatoes, and avocado to a large bowl. Toss the salad with the dressing until combined. Serve with lime wedges and garnish with parmesan shavings.