Break off a few crumbs of yeast from the yeast cube. Mix the yeast, water, and flour to form a pre-dough. Let rise at room temperature for 1 hour.
Knead the pre-dough again. Let rise for another 1 hour or until the dough has visibly doubled in volume.
Cut the tomatoes, peppers, and ham or salami into small cubes and set aside.
Divide the dough into 12 equal portions. Roll each into a round shape. Place a tablespoon of filling on each round, then close and seal the edges to form a calzone.
Drizzle both sides of each calzone lightly with olive oil.
Heat a charcoal grill to high heat. Place the calzones on the grill and grill on both sides for about 15 minutes total until cooked through.