Heat a large skillet over medium heat. Toss kale in the skillet; cook and stir until reduced in size by about one-quarter, 1 to 2 minutes.
Remove kale to a bowl; refrigerate for 1 hour.
Beat mayonnaise, olive oil, mustard, Parmesan cheese, lemon juice, garlic, Worcestershire sauce, and anchovy paste together in a bowl until you get a smooth salad dressing; refrigerate for 1 hour.
Toss kale, cucumber, and leeks together in a large bowl.
Drizzle dressing over the salad; toss. Season with black pepper.