Preheat broiler. Combine pork, stock, half the onions, the jalapeno, cilantro, cumin, bay leaf, and 1/2 teaspoon salt in a medium saucepan. Bring to a boil. Reduce to a simmer. Cook, stirring occasionally, until pork registers 140 degrees on an instant-read thermometer, 10 to 15 minutes.
Transfer pork to a rimmed baking sheet. Shred into 2-inch pieces with 2 forks. Add remaining onion. Stir in butter and oil. Season with salt and pepper. Broil pork until golden brown, 4 to 7 minutes.
Top each corn cake with 3 avocado slices, heaping 1/3 cup pork, 2 tomato wedges, and 1 tablespoon sour cream. Garnish with cilantro.