Beat the eggs and oil in the bowl of your stand mixer, fitted with the balloon/whisk attachment, for a short time. Pour in the buttermilk-yeast mixture and beat on low to combine.
Transfer the pan to a wire rack to cool, in the pan, for about 20 minutes, but first, baste the top with melted butter if you prefer a soft, tender crust. The steam that develops in the pan will soften the side and bottom crust a little. If you prefer a crunchy crust, immediately remove the bread from the pan and transfer to the wire rack to cool completely. For softer crust, wait the 20 minutes before transferring.
Slice once the bread is completely cool, for about 90 minutes.
Use 2 tablespoons bean liquid from a can of white beans (like cannellini) to replace each large egg white and 1 tablespoon butter or other fat like coconut oil (refined for flavor-free) to replace each large egg yolk.
See the Substitutions page for dairy-free substitutions including dairy-free buttermilk.