Heat the olive oil in large pot over medium low heat. Add the onions and raise the heat to medium, then sauté until softened and translucent and some pieces turn lightly golden around the edges, about 10 to 15 minutes, stirring every 4 minutes or so. Add the garlic and stir to incorporate and cook for another 5 minutes. Add the carrot, celery, 2 teaspoons of the thyme, and the bay leaf and stir to combine. Allow to cook for another 10 minutes, stirring every 5 minutes or so.
Nestle the ham hock in the vegetable mixture, then add the split peas and the broth and reduce heat to low. Cover the pot and allow to cook until the split peas have mostly disintegrated into the soup mixture, about 1 hour to 1 hour 20 minutes, stirring every 15 to 20 minutes.
During the last 30 minutes of soup simmering, you can prepare the seared shallots. Heat the oil in a cast iron skillet over medium heat. Add the shallots, cut-side facing down, and cook until lightly golden and fragrant on each side. Remove from heat and set aside.
Remove the ham hock from the soup and place it on a wooden cutting board. Remove any meat pieces from the hock and chop the meat into roughly 1/2-wide cubes.
Stir the pieces of meat into the soup, remove the pot from heat, and immediately stir in the fresh or frozen peas, the remaining 2 teaspoons of thyme, and the parsley. Taste and add salt and pepper to your liking. Serve with the toasted pumpkin seeds and seared shallots on top and some good bread on the side for dipping.