Cover the ham hocks with cold water in a soup pot. Bring the mixture to a boil, reduce the heat, and simmer, uncovered, about 5 minutes. Drain the water, set the hocks aside.
Meanwhile, peel the shrimp, reserve the shells. Devein the shrimp and refrigerate.
Heat 1 tablespoon of the oil in a soup pot over medium heat; add the shrimp shells and tomato paste, and cook, stirring, until the shells turn pink, about 3 minutes. Add the ham hocks, halved garlic, thyme, lemon zest, and 3 quarts cold water. Bring to a boil, then reduce the heat to maintain a simmer. Cook, uncovered, until the meat falls off the ham hock, about 1 1/2 hours.
Strain the broth into a bowl (you should have about 6 cups broth), and save the ham hocks. When the ham hocks are cool enough to handle, pull the meat from the bone; discard the rind, fat, and bone. (This can be done a day ahead.)
In a large soup pot, heat the remaining 2 tablespoons oil over medium heat. Add the onion, sliced garlic, and 1/2 of the jalapeno. Crush the tomatoes through your hands and add to the pot along with their juices and cook until onions soften and tomatoes dry, about 10 minutes. Add the broth, ham, black-eyed peas, and bring to a boil, adjust the heat to maintain a simmer, and cook, uncovered, until the peas soften, but hold their shape, about 20 minutes. Add the escarole, and the remaining jalapeno, and cook until the greens wilt, about 7 minutes. Stir in the shrimp and 1 1/2 teaspoons salt, and cook until the shrimp turn pink and curl, about 3 minutes. Divide the soup evenly into warmed bowls. Serve with a lemon wedge.
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