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1
Skim all orange fat from the surface of the consomé into a separate shallow pan; reserve the consomé in a separate vessel. Set both over the lowest possible heat. The fat should remain liquid and deeply orange — this is the dipping medium for the tortillas, not the broth itself.
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2
Heat a cast-iron griddle or heavy flat pan over medium-high heat until a drop of water skitters and vanishes on contact. Working one tortilla at a time, dip both faces of the tortilla into the pan of orange fat, coating evenly. Lay the tortilla on the griddle. It should sizzle immediately and begin to colour red-orange on the underside — this is the moment the dish lives or dies: the fat must be the dipping medium, never the broth, and the griddle must be hot enough to crisp, not steam. A tortilla dipped in broth will go soft and collapse; a correctly fat-dipped tortilla will become a rigid, orange-lacquered shell.
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3
While the first side crisps, lay a portion of shredded birria — warm and saucy — across one half of the tortilla. Cover the meat with a generous layer of cheese. Press the taco flat against the griddle with a spatula, holding it down so the cheese makes full contact with the hot surface and begins to melt into the meat.
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4
When the cheese has melted and the underside of the tortilla is firm and deeply coloured — lift one edge to check — fold the empty half over the filled half. Press gently. The taco should close cleanly without bursting. Transfer to a warm plate and repeat for remaining tortillas.
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5
Ladle the consomé into individual cups or bowls, serving it steaming hot. Garnish each with diced white onion, chopped cilantro, and a lime wedge. The consomé must be at a full serving temperature — steam should rise visibly from the cup. Set one cup beside each plate of tacos for dunking.