Place crushed red pepper in a small dry skillet over medium heat. Toast for 90 seconds, stirring frequently. Remove pan from heat and let cool.
Cut melon in half lengthwise, remove and discard seeds, and quarter lengthwise. Remove the peel. Shave the melon into strips using a vegetable peeler. Arrange melon strips and ham slices on a platter. Crumble the burrata evenly over top and sprinkle with toasted red pepper and cracked black pepper. Drizzle vinaigrette over top. If using, garnish with fresh basil right before serving.