Brown the ground beef hard in a dry heavy pot over high heat, in two batches so it colours instead of steaming. Lift it out and set aside.
Melt the tallow in the same pot and brown the diced chuck on all sides. Do not rush this, the dark crust stuck to the pot is the flavour.
Return the mince, pour in the bone broth, add the salt (and cayenne if using), and scrape up every browned bit from the bottom.
Bring to a bare simmer, cover, and cook low for 1.5 to 2 hours, until the chuck is fork-tender and the fat has emulsified into the sauce.
For a thicker chili, take the lid off for the last 20 minutes, or whisk the egg yolks into a ladle of the warm (not boiling) liquid and stir it back in.
Taste, add more salt, and serve with grated cheddar and soured cream if you want them.