Preheat the oven to 350 degrees F. Line a rimmed baking sheet with parchment paper.
Lay the prosciutto slices on the parchment without touching.
In a small bowl, mix together the sugar, salt, allspice and cayenne.
Brush each slice of prosciutto with some olive oil and sprinkle with the spice mix.
Place the baking sheet in the preheated oven and bake until the ham is beginning to crisp and the sugar is caramelized, 16 to 18 minutes.
Transfer the slices to a cooling rack to cool completely. Blot with a paper towel if beads of oil form.