1. Heat up grill to medium-high heat, or an oven to 400°F.
2. Unroll the refrigerated Classic Pizza Dough and leave it on parchment paper to season. Cut in 4 strips, lengthwise, and brush with 2 Tbsp. green pesto.
3. Distribute ham and cheese evenly to center of the 4 dough strips. Brush one side with egg and fold dough over, to get a stuffed long dough log, seam is facing down.
4. Score top of dough diagonally with a small sharp knife, about every 1/2 in. Roll up half of the dough log, then roll up the other half in the opposite direction to create a S-shaped roll.
5. Brush with beaten egg, and grill for about 10-15 min. with grill pan (covered grill, no parchment paper), or bake in oven with parchment paper on baking pan for about 13 min. or until golden brown.