Preheat the oven to 230°C (gas mark 8) and place a pizza stone inside if you have one.
Lightly flour a clean surface and stretch the pizza dough into a 30 cm circle.
Transfer the dough to a pizza peel or a baking sheet lined with baking paper, then brush the edges with olive oil.
Sprinkle half of the shredded mozzarella and Monterey Jack cheese evenly over the dough, leaving a 1 cm border.
Evenly spread the shredded birria meat over the cheese.
Sprinkle over the remaining mozzarella and Monterey Jack cheese.
Scatter half of the diced onion and half of the chopped coriander over the top.
Slide the pizza onto the hot stone or place the baking sheet in the oven and bake for 12–18 minutes, until the crust is golden and the cheese is bubbling.
While the pizza bakes, warm the birria consommé in a small saucepan over a low heat until hot but not boiling.
Remove the pizza from the oven and leave to rest for 1–2 minutes, then slice.
Scatter the remaining onion and coriander over each slice and serve with the warm consommé for dipping.