Preheat the oven to 350°. Spread the walnuts in a pie plate and toast them in the oven for 10 minutes, until fragrant and golden. Let cool, then coarsely chop the nuts.
In a food processor, pulse the mayonnaise, buttermilk, shallots and vinegar until smooth. Add the blue cheese; pulse until chunky. Add the walnuts and pulse until fine. Season with salt and pepper; garnish with the chives.