Heat oil in nonstick pan over medium heat. Add shallots; cook until transparent. Add mushrooms; cook 3 minutes, stirring. Add parsley and lemon juice. Season to taste with salt and pepper. Remove from heat. Stir in turkey.
Tear or cut radicchio into small pieces and use to line a serving platter. Top with turkey and mushroom mixture. Cut plums into thin slices and add to salad.
To make cheese dressing, beat cheese, 3 tablespoons milk and vinegar in a bowl until well combined. If mixture is not sufficiently runny, add remaining 1 tablespoon milk. Add salt and pepper to taste. Drizzle dressing over salad. Garnish with walnuts.