Spread the pine nuts on a rimmed baking sheet and bake until lightly toasted, about 5 minutes.
Fill a large bowl or pot with very hot tap water. Add the kale and stir for a few seconds just to slightly soften the leaves. Drain and squeeze well to dry. Gather and stack the kale leaves on top of each other on a cutting board, roll them up and thinly slice.
Mash the anchovy and garlic to a paste on a cutting board with the flat side of a knife. Transfer to a small bowl and add the lemon juice, 1/4 teaspoon salt and a few grinds of pepper. Whisk in the olive oil.
Toss the kale with the Parmesan and pine nuts in a salad bowl. Add just enough vinaigrette to coat, tossing well to combine. Top with the basil.