Make the dressing:
Combine the shallots, lemon juice, and 1/2 tsp. salt in a small bowl, and let sit 5 minutes. Whisk in the crème fraîche and buttermilk, then the mayonnaise. Adjust seasoning with salt and pepper to taste.
Assemble the salad:
Position a rack in the center of the oven and heat the oven to 375ºF.
Spread the walnuts on a baking sheet and toast them, stirring once or twice, until they smell nutty and are lightly browned, 8 to 10 minutes. When the nuts have cooled slightly, toss them with the olive oil and a generous pinch of salt. Crumble half of them with your hands.
Cut the apples into 1/8-inch slices and put them in a large salad bowl. Dress the apples with half of the buttermilk dressing and then very gently toss in the arugula, radicchio, and mint. The salad should be lightly dressed—add more salad dressing only if needed (you will have leftover dressing, which will keep for a few days in the fridge).
Arrange the salad on six plates and scatter the toasted walnuts (both crumbled and whole) over the top.
Make Ahead Tips
The dressing may be made a day ahead.
nutrition information (per serving):
based on six servings;
Photo: Scott Phillips