Heat oven to 400° F.
Roll the pizza dough into a 14-inch circle and cut into 8 triangles.
Stack a piece of the ham, cheese, and onion on the bottom of each triangle and roll the dough up around the filling. (Some of the filling will stick out the ends.)
Transfer the rolls to a parchment-lined baking sheet. Bake until golden and crisp, about 20 minutes.
Combine the mustard and oil in a medium bowl and toss with the romaine. Serve with the turnovers.
Make Ahead: These turnovers can be assembled, wrapped tightly, and then refrigerated up to 12 hours in advance. Once cooked, they will last for up to 5 days in the refrigerator if sealed tightly in bags or containers. Reheat in a 350° F oven until warm.