Add a handful of grated parmesan, the pine nuts, the boiling water, and 1/4 stock cube to the blender. Blend until smooth, then season to taste. (Set aside a small amount of pesto for topping later.)
Stir the pesto through the cooked fregola and warm it briefly over low heat.
Divide the fregola between plates. Tear open the burrata and spoon some of the creamy center over the fregola. Season with salt and pepper, drizzle with extra pesto and olive oil, and finish with pistachios and a little extra grated Parmesan.