Start by soaking the beans in water for 8 hours. You need enough water to generously cover the beans, approx. 4 inches above the beans in the container.
When the beans have softened, drain them and set aside.
In your small pot, add a little bit of canola oil, the garlic, the onions, and the fennel. Turn on the heat to medium and sweat down until they become translucent. This technique is called sweating and is very common in making beans, soups, stews, etc.
Add the black eyed peas, and cover the peas with water. There should be nearly an inch of water above the black eyed peas. Add the sherry vinegar and some salt. Reduce the heat to low. Cook for 1 1/2 - 2 hours, adding water, splashes of sherry vinegar, and salt as you go. Through this process of tasting the beans, you should be tasting for a creamy bean consistency, with a nice and underwhelming acidity from the sherry vinegar, a mild saltiness. Be careful when adding the sherry vinegar. This is only used to "brighten" up the flavor of the beans.
When you bite into the beans and they are creamy and smooth (on the inside), add your butter, parsley, and lemon juice to finish. Stir the cold butter in with the heat off. This is called mounting. This technique is done in french cooking when finishing sauces such as beurre blancs, meat sauces, or beans in this nature.