First, in a large heavy-bottomed pot, melt the butter and mix in the oil. Add the carrots and sauté for a minute or two. Then add the onions, stir, and sauté everything for 3 or 4 minutes, until the onions are translucent and limp.
Pour in the peas, stir, then add the broth and water, the hock (or the chopped ham), bay and savory. Give it all another stir, bring to the boiling point, then simmer gently. Stir every now and then to avoid sticking. This will take two or three hours. You may need to add more liquid if the soup gets too thick before it’s done.
Once the peas are cooked, remove the ham hock, strip off the meat, chop it and return it to the pot. Taste and season with salt, if needed. You likely won't need it—the ham hock will add plenty of its own.