Add the butter to the flour mixture and cut it into the flour mixture using either the rubbing method or a pastry cutter.
When the pastry has chilled, place it on a floured surface and roll it out to ⅛" thickness. ransfer the pastry to a 9" pie plate and crimp the edges.
When the oven is up, line the pastry with parchment paper and pour in a bag of dried beans. Bake the pastry for 17-20 minutes.
Place the eggs, milk, cream, mustard, and salt in a large bowl. Whisk until frothy. Fold in the shallots, peas, scallions, dill, parsley, and mint.
Pour the filling into the pastry shell and transfer to the oven. Bake for 45 minutes or until the edges are set but the center is still a little jiggly.
Place the burrata in the center of the quiche and top with Calabrian chilis. Finish a drizzle of the chili oil.