PREP THE CHILLIES FIRST. Cut the anchos into 2-3 pieces.
Heat a medium sized frying pan on medium-low heat and dry roast the chillies for 2-3 minutes. Don't burn them, as your birria will end up bitter. Toss your chillies every now and then to brown evenly.
Drop them into a roomy bowl and pour a generous amount of boiling water all over. Cover with a plate and leave to soak for 20 minutes.
PREP THE DRY SPICES & GARLIC. While the chillies are soaking, dry fry the cumin seeds, thyme, oregano, bay leaves and sesame seeds in the same frying pan on medium-low heat for 3 minutes, tossing frequently.
Tip out onto a plate or add straight to your spice mill (or blender). I like to grind the dried spices and bay leaves in a spice mill into a powder before adding to the blender to make the birria adobo. But if you don't have a spice mill, or can't be bothered, add straight to your blender.
Finally, dry fry the garlic cloves in the same pan. We want to char it slightly. Do this for 2 minutes, until you get brown spots on the garlic. Tip into the blender (NOT the spice mill).
MAKE THE ADOBO. Drain the chillies, reserving the soaking liquid (you'll only need a little. Place the chillies in your blender. Follow this with everything else: the dried spices, bay leaves (whether you ground them earlier or not), garlic, salt, clear vinegar, balsamic vinegar.
Blend everything until you get a fairly smooth paste. Add some of the soaking liquid if you need it.
Brown and Marinate the Meat
Season the beef ribs with salt and pepper. Then brown them in a large frying pan on medium-high heat, in a single layer. Don't overcrowd. Do this for 2-3 minutes each side. You'll find this will render some of the fat on the ribs, which will add flavour to our birria. Transfer to an ovenproof casserole dish or dutch oven. Repeat with the rest of the ribs.
Now pour the chilli adobo all over the browned ribs (or whatever meat you are using), and stir with a wooden spoon to coat all the ribs. Cover, and place in the fridge to marinate overnight. Or 2 hours at the very least.
The Next Day (Day 2)
Preheat the oven to 180°C (350°F/Fan 160°C).
Top the adobo-covered beef with everything else: quartered onion, garlic and bay leaves.
Add water along the inner side of the saucepan until the liquid comes up to about 1 inch above the meat. Don't "rinse" and wash away the adobo off the meat.
Place your casserole dish containing the marinating beef into the oven and cook for 4 hours. Make sure that your dish is covered, with a lid or foil. I covered my copper pan with foil as the lid is glass.I usually take the lid off for the last hour, to allow the sauce to thicken, as I like it thick when eaten with rice. I shall leave this up to you. And if you want the sauce much lighter, you can always add some water.
When done, top with some freshly ground black pepper, stir in 1 Tbsp of lime juice and check the seasoning. Add more salt if you think it needs it. Leave to rest, covered for 10 minutes before serving. Serve as described in the post above.
On the Stove Top
Instead of placing in the oven, you can cook your birria on the stove top. Bring it to a boil then lower the heat right down, cover and cook for 2½-3 hours, until the meat is soft and falling of the ribs.