Combine kale, 2 tablespoons oil and ¼ teaspoon salt in a large bowl. Using your hands, massage the kale until well coated, about 1 minute.
Whisk vinegar, mustard, pepper and the remaining ¼ teaspoon salt in a small bowl. Whisking constantly, slowly drizzle in the remaining 3 tablespoons oil.
Add strawberries, goat cheese and walnuts to the kale; drizzle the dressing over the salad and gently toss to combine.
