In a large pot or Dutch oven, combine the rinsed split peas, water, and salt.
Bring to a rolling boil over high heat, then reduce the heat to low, cover, and let it simmer for about 1 hour. Use a spoon to skim off any foam that rises to the surface.
While the peas are simmering, melt the butter in a large skillet over medium heat.
Add the chopped carrots, sweet potato, onions, and celery.
Sauté for 10 minutes, stirring frequently, until the vegetables have softened.
Stir the minced garlic, marjoram, basil, and cumin into the vegetables and cook for another 2 to 3 minutes until fragrant.
Carefully transfer the cooked vegetable mixture into the pot with the simmering split peas.
Stir to combine, and continue to simmer, partially covered, for another 45 to 60 minutes, stirring occasionally to prevent sticking. The peas should be very tender.
For a creamier texture, carefully transfer about half of the soup to a blender and purée until smooth. Return the puréed soup to the pot. Alternatively, use an immersion blender directly in the pot and pulse a few times until you reach your desired consistency.
Stir in the dry white wine and season generously with fresh black pepper.
Bring the soup back to a gentle simmer for a few minutes to allow the flavors to meld.
Taste and adjust salt if needed.
Ladle the hot soup into bowls and serve immediately, garnished with croutons if desired.