Preheat the oven to 350°F. Pour the Pistachios onto a sheet pan and toast in the oven for 5 to 10 minutes. Remove and transfer 4 tablespoons of the Pistachios to a blender or food processor. Add the oil, vinegar, ⅓ cup water, basil, salt, and pepper to taste, and blend the vinaigrette until smooth. Finely chop the remaining 2 tablespoons of Pistachios and add to the vinaigrette. Keeps well if refrigerated for up to 3 to 4 days.
Cut beetroot into quarters. Transfer the beets to a serving platter with basil, torn burrata, quinoa, Pistachios and pomegranate seeds and drizzle with Pistachio vinaigrette. Season with salt and pepper and serve immediately.
