Stir together all of the ingredients and set them aside.
Make the Toasted Walnut Vinaigrette
In a food processor, pulse 1/2 cup of the toasted walnuts, garlic, olive oil, capers, and honey together until the nuts are in small pieces. Transfer to a bowl and stir in the vinegar; season with salt and pepper.
To assemble the Holiday Salad with Citrus
Preheat the broiler to high and move one rack to the top position closest to the broiler. Place the prepared grapefruit on an aluminum foil-lined baking sheet and char for 7-12 minutes, turning occasionally. Cool to room temperature.
Toss the shaved carrots with 2 tablespoons of the prepared Toasted Walnut Vinaigrette, set aside to marinate.
When the citrus is cool enough to handle, segment the grapefruit into supremes over a bowl so that all of the juices are collected. Add the fresh orange and mandarin segments to the bowl and toss to combine with the juice of the broiled grapefruit.
In a separate bowl, toss the arugula and parsley with a few tablespoons of dressing. Chop the remaining 1/4 walnuts.
To serve, smear the prepared yogurt across the bottom of the serving platter. In alternating layers, pile on the carrots, arugula, chopped toasted walnuts, and citrus segments.
Repeat layering ingredients thinly on top of each other until all of the ingredients have been used the sprinkle the top of the salad with crispy shallots to serve.
Notes
To toast walnuts:
Preheat the oven to 350°F. Toast walnuts on a rimmed baking sheet, tossing halfway through, until slightly golden and fragrant, about 8-10 minutes. Let cool.