Heat a skillet or comal over medium-high heat. Roast the Roma tomatoes, jalapeño, garlic, dried chile japones entero pods, and dried pasilla ancho entero pods until lightly charred.
Transfer the roasted vegetables and chiles to a blender with the beef broth, chile adobo molido, cumin, oregano, salt, and pepper. Blend until completely smooth.
Strain the mixture through a fine-mesh sieve into a saucepan. Simmer over medium-low heat for 15–20 minutes, stirring occasionally, until slightly thickened. Keep warm.
Heat a large skillet over medium heat and lightly grease. Dip the tortillas in the birria consommé. Then place them on the warm skillet. Sprinkle a generous layer of BelGioioso Quesadilla Cheese over the whole face of each tortilla, then top with shredded birria beef. Fold the tortilla in half.
Cook for 2–3 minutes per side, until the tortillas are golden and crispy and the BelGioioso Quesadilla Cheese is fully melted.
Top each taco with diced onion and fresh cilantro.
Serve immediately with the warm birria consommé for dipping and fresh lime wedges on the side.