Stand leeks in small baking pan with oil, salt pepper and butter. Cover with foil and roast until deeply caramelized and tender. Let cool slightly.
Make gremolata by putting pistachios, parsley, lemon zest, salt, pepper, and garlic in a blender, and blend until slightly chunky.
Spread gremolata on platter, and layer arugula, torn burrata, and warm leeks over top.
In the leek baking pan, mix the leftover juices with olive oil, red wine vinegar, and chopped parsley. Spoon vinaigrette over the dish, and finish with any remaining gremolata & flaky salt.