Thoroughly drain corn, then add to a large pot in a single layer and heat over medium-high heat undisturbed for 2-3 minutes. Stir and char an additional 2-3 minutes, then remove and set aside.
Add sausage slices in a single layer, then cook over low to medium heat for 5 minutes or until browned on both sides. Use a slotted spoon to remove sausage and set aside.
Dice onions and add to pot; sauté over medium heat for 5-7 minutes or until softened and lightly golden, stirring occasionally. Add thinly sliced garlic and toast for 2 minutes, then deglaze with white wine. Add diced potatoes, broth, smoked paprika, and bay leaf. Bring to a gentle boil, then cover and simmer over low heat 15 minutes or until potatoes are fork-tender.
Remove bay leaves, then blend soup using an immersion blender until smooth. Add corn, chopped kale (spines removed), Calabrian chili paste, sliced pickled carrots, and chorizo sausage. Heat for an additional 3 minutes, then season with salt and pepper to taste.
Notes
I'm using fully-cooked sausage, so cook times may vary if meat is raw. If your sausage isn't oily enough to get a good char, you can add 1 tablespoon olive oil.
This soup is pretty thick, much like a stew, but you can thin it out with additional broth or even water if you prefer.
Store leftover chorizo soup in the refrigerator in an airtight container for 3-4 days.
Reheat in the microwave or over medium-low heat on the stovetop.
I wouldn't recommend freezing this soup, as the texture would change drastically.