This has been hurting my brain for a while.
A science fiction/fantasy novel probably written after 2000. Opens in the American West with a farmsteader pursuing a wealthy outlaw after a train robbery and murder of the farmsteader’s wife. The outlaw escapes into the desert and discovers a cave containing an egg that causes him to be reborn as a fully grown adult with all memories whenever he dies. The farmsteader later gains the same power. Story spans three eras (Old West, around the 1930s/40s, and modern day). Sometimes duplicate versions of the characters are reborn and diverge. There is a giant dead grasshopper in the cave, possibly a giant eagle near the end, and the climax involves an interdimensional being explaining the egg could destroy the universe unless one protagonist sacrifices himself/worlds to stop it.