Drain both cans of seasoned black-eyed peas. Process one drained can in a food processor until fairly smooth and transfer to a medium bowl. Pat the other can with paper towels to remove extra moisture and add the whole peas to the bowl.
Melt 1 tablespoon butter in a large nonstick skillet over medium heat. Add the chopped onion and red bell pepper and cook for about 5 minutes until softened.
Add sliced green onions and minced garlic to the skillet and cook 1 more minute. Remove from heat, let cool slightly, then add the vegetable mixture to the bowl with the black-eyed peas.
Stir in 1 1/2 cups cornbread crumbs, 1 egg yolk, and 1 teaspoon cumin until the mixture is evenly combined.
Form the mixture into patties about 2 1/2 inches across. Lightly dredge each patty in 1/2 cup cornmeal and place on a baking sheet. Refrigerate the patties for at least 1 hour to firm up.
Heat 3 tablespoons vegetable oil in a large nonstick skillet over medium-high heat. Fry the chilled patties in batches for about 2 minutes per side, until golden brown. Remove and drain on paper towels.
Meanwhile, mix 1/2 cup sour cream with 2 teaspoons diced pickled jalapeños. Serve the jalapeño sour cream with the black-eyed pea cakes.