Make the cashew cream: Blend cashews, water, and a pinch of salt until silky smooth. Set aside 3/4 cup for the soup.
Sauté the base: Heat olive oil in a large pot over medium heat. Add onion and celery, cooking until tender (5-7 minutes). Stir in garlic and cook for another minute.
Add the bulk ingredients: Pour in vegetable broth, yellow split peas, chopped potato, corn, paprika, and sea salt. Bring to a boil.
Simmer: Reduce the heat to low, cover, and let the soup simmer for about 45 minutes, stirring occasionally. The split peas should be completely soft.
Blend for texture: Use an immersion blender to partially puree the soup, or blend half of it in a standard blender and return it to the pot.
Finish with flavor: Stir in the reserved cashew cream and apple cider vinegar. Taste and adjust with more salt if needed.
Serve: Ladle into bowls while hot and garnish with your favorite toppings, like crispy coconut bacon or fresh herbs.