In a large pot, heat a bit of vegetable broth over medium heat. Add the chopped onion, carrots, and celery. Sauté for about 5 minutes until the vegetables start to soften.
Add the minced garlic and continue to sauté for another minute until fragrant.
Stir in the dried split peas, bay leaf, and dried thyme. Pour in the vegetable broth, and bring the mixture to a boil.
Reduce the heat to low, cover the pot, and let it simmer for about 30 minutes. Stir occasionally to prevent sticking.
Add seasonings of thyme, smoked paprika, coconut aminos, and the diced potatoes to the pot, and continue to simmer for another 20-30 minutes, or until the split peas and vegetables are tender and the soup has thickened. You can adjust the consistency by adding more vegetable broth if needed.
Remove the bay leaf from the soup and discard it.
If you want a smooth soup, use an immersion blender to partially blend the soup. You can blend it until it's as smooth or as chunky as you prefer. Alternatively, you can transfer a portion of the soup to a blender and blend until smooth, then return it to the pot.
Season the soup with salt and pepper to taste. Adjust the seasonings as needed.