How to Make It
Place crushed red pepper in a small dry skillet over medium heat. Toast 90 seconds, stirring frequently. Remove pan from heat; cool.
Combine vinegar, shallots, honey, and salt in a small bowl, stirring with a whisk. Slowly add oil, stirring constantly with a whisk.
Cut each melon in half lengthwise; remove and discard seeds, and cut melons into quarters. Shave 1 quarter of each melon into strips using a vegetable peeler to yield about 1 1/4 cups cantaloupe and 1 1/4 cups honeydew. Reserve remaining melon for another use. Arrange melon strips and ham slices on a platter so they overlap or intertwine. Spoon burrata evenly over top; sprinkle with toasted red pepper and cracked black pepper. Drizzle vinegar mixture over top.