AT HOME (UP TO 1 DAY AHEAD)
Preheat oven to 350°. Toss walnuts with 1 tbsp. olive oil and spread out evenly on a baking sheet. Bake until a rich golden brown and very fragrant, about 12 minutes. Let cool slightly, then roughly chop enough walnuts to measure 1/4 cup. Reserve remaining halves.
Whirl together remaining 3 tbsp. olive oil, the vinegar, walnut oil, mustard, yogurt, and salt in a blender just until smooth. Add chopped walnuts and whirl quickly just to blend (you want the walnuts to stay chunky). Pour into a jar with a tight-fitting lid.
Tear kale into bite-size pieces (discard stems or save for another use) and put in a resealable plastic bag; chill kale and dressing until you leave.
AT THE PARTY
Toss kale well with dressing in a large bowl. Let sit at least 10 minutes and up to 30, tossing occasionally (this helps soften the kale slightly).
Slice apple and add half the slices, along with half the reserved walnut pieces, tossing to coat. Transfer salad to a large platter. Sprinkle with remaining apple slices and walnuts.
*We like La Tourangelle brand, available at well-stocked grocery stores.