Make the cashew cream. Combine the cashews, water, and salt in a blender and process until very smooth. Set 3/4 cup aside.
Heat the oil in a large pot over medium heat. Add the onion and celery and cook, stirring occasionally, for 5 to 7 minutes, until the onion is tender and translucent. Add the garlic and cook, stirring constantly, for 1 minute.
Stir in the broth, split peas, potato, corn, paprika, and salt and bring to a boil over high heat. Lower the heat, cover, and simmer, stirring occasionally, for about 45 minutes, until the split peas are completely tender.
Use an immersion blender to partially puree the soup, or puree about half of it in a regular blender and return it to the pot. Stir in the Cashew Cream and apple cider vinegar. Taste and adjust the seasonings if desired. (I added up to 1 teaspoon more sea salt here). Serve piping hot, with any desired toppings.