Cut each beef short rib through the middle, all the way down to the bone. Cut beef chuck in half; cut each half into 3- to 4-inch pieces.
Place beef chuck and short ribs into a soup pot and season with salt, black pepper, oregano, cumin, cinnamon, and cloves. Toss very thoroughly until the meat is evenly coated with the spices, 2 to 3 minutes.
Cover and transfer into the refrigerator for at least 6 hours, or overnight.
Prep guajillo chiles by snipping off stems with scissors; slice open and scrape or shake out the seeds onto a plate to discard.
Heat olive oil in a saucepan over medium heat. Add dried guajillo chiles and toss in the hot oil, about 30 seconds. Add chopped onion, garlic, and ginger; toss to combine. Add tomatoes and water, raise heat to high, and bring the mixture to a simmer. Reduce heat to medium-low and let simmer for 30 minutes.
Turn off heat and use an immersion blender to blend the mixture as smooth as possible, or transfer to a regular blender, working in batches as needed.
Remove the soup pot with meat from the refrigerator. Strain the reserved chili mixture into the pot using a large mesh strainer. Add bay leaves, honey, vinegar, and chicken broth.
Bring to a boil over high heat, and then lower to medium-low. Simmer gently, stirring occasionally, until the meat is falling-apart tender, 3 to 4 hours. Skim fat off of the top and reserve for future birria queso tacos.
Place some chunks of beef into a soup bowl and ladle some of the cooking liquid over top. Top with white onion and chopped cilantro and squeeze lime juice over top.