Broil the tomatoes, jalapeño and onion 5 inches from the heat for 6 to 8 minutes until blistered and softened.
Pulse the roasted vegetables with the lime juice and 1/4 teaspoon salt into a chunky salsa, then drain any watery liquid.
Mix the chorizo, ground pork, cumin and remaining salt just until marbled together and shape 4 patties.
Cook the patties in a skillet over medium heat for 6 to 7 minutes on the first side without pressing.
Flip and cook for 5 to 7 minutes more until the centers reach 160°F.
Top each patty with Monterey Jack, cover for 1 minute and toast the split rolls alongside them.
Build each burger with shredded cabbage, one pork patty and 2 tablespoons drained roasted tomato salsa.