Cut both ends off of the onion. (Root and top). Cut the onion in half lengthwise.
Peel the onion halves from their shell and outermost layer, then lay cut side down onto a cutting board.
Thinly slice the onions into 1/8" slices, cutting with the natural lines of the onions to create half moons.
Heat a pan over medium heat. Add olive oil and butter, and allow to melt and completely heat through.
Scatter the onion slices into the pan, and toss to coat the onions in the butter and olive oil. Sprinkle the onions with kosher salt, then stir to coat the slices in salt.
Allow to cook for ten minutes at medium heat. Stir to redistribute the onions, and turn the heat to medium-low.
Stir every ten to fifteen minutes to encourage even caramelization, for a total of about thirty to forty minutes.
(OPTIONAL) Once the onions are almost entirely browned, add the sherry vinegar and freshly cracked black pepper. Stir to mix into the onions, and allow to cook an additional five minutes.
Remove the onions from the heat, and allow them to cool for about fifteen minutes before transferring them to a lidded container.
Store for up to four days in the refrigerator, or freeze for up to three months.