In a large bowl, whisk together the olive oil and balsamic vinegar. Season with a punch of red pepper flakes, salt and pepper.
Slice the radicchio into thin ribbons. Add to the vinaigrette and roughly toss together with tongs. Let this sit and marinate while you finish up the other ingredients.
Lay half the bread out on a work surface. Top each piece with a thin layer of prosciutto, scatter the chopped artichokes on top, and then add the burrata. Add the parsley to the radicchio mixture, toss to combine, and place on top of the burrata. Finish with the arugula and top with the remaining slices of bread.