Cut beef chuck in half; cut each half into 3- to 4-inch pieces. Cut each beef short rib through the middle, all the way down to the bone.

Place beef chuck and short ribs into a soup pot; season with kosher salt, oregano, black pepper, cumin, cinnamon, and cloves. Toss thoroughly until meat is evenly coated with spices, 2 to 3 minutes. Cover and keep in the refrigerator for at least 6 hours to overnight.

Prep guajillo chiles by snipping off stems with scissors; slice open and scrape or shake out seeds onto a plate to discard.

Heat olive oil in a saucepan over medium heat. Add guajillo chiles and toss in hot oil, about 30 seconds. Add onion, garlic, and ginger; toss to combine. Add tomatoes and water; bring to a boil. Reduce heat to medium-low and let simmer for 30 minutes.

Turn off heat and use an immersion blender to purée mixture as smooth as possible, or use a countertop blender, working in batches as needed.

Remove the soup pot with meat from the refrigerator. Strain puréed chili mixture into the pot using a large mesh strainer. Add chicken broth, vinegar, bay leaves, and honey to the pot.

Bring to a boil, then reduce heat to medium-low. Simmer gently, stirring occasionally, until meat is fall-apart tender, 3 to 4 hours. Skim fat off of the top and reserve for future birria queso tacos.

To serve, place a few chunks of beef into a soup bowl and spoon some cooking liquid on the top. Sprinkle with some white onion and cilantro; squeeze lime juice over the top.