First, prepare your vinaigrette. In a small bowl, combine the red wine vinegar and shallot. Let it sit for 10 minutes. Add the salt and pepper, then slowly drizzle in the olive oil, whisking as it emulsifies. Set aside.
In a large mixing bowl, start layering the radicchio, wild arugula, parsley, radish, shallot, pistachio, tangerine, and crumbled feta. Continue layering until all ingredients have been used up. Start to drizzle the salad with the dressing and gently toss to coat the ingredients. Taste. Continue adding the vinaigrette as needed and season with any additional salt and black pepper if necessary. Transfer the salad to a serving bowl and serve.