Preheat oven to 350°F. Grease a 13"-by-9" baking pan with cooking spray or vegetable oil.

Place one unrolled can of crescent dough in prepared baking pan, pinching together seams if necessary, and slightly stretch to fit pan. Bake until lightly golden, 8 to 10 minutes. Let cool slightly, about 5 minutes.

Sprinkle 1/2 cup Asiago in an even layer over baked dough, leaving a 1/2" border around the edge of dough. Top with layers of mortadella, provolone, salami, giardiniera, and remaining 1/2 cup Asiago.

Unroll remaining crescent dough to cover filling. Pinch edges of top and bottom doughs together to seal. Brush top of dough with oil. Sprinkle with sesame seeds and oregano.

Bake, covering with foil if dough is browning too quickly, until dough is golden brown and cooked through, 30 to 35 minutes.

Let cool at least 15 minutes before slicing into squares.