Cook the sausage (crumbling it) over medium heat until brown. Place the sausage in the slow cooker.
Sauté the white onion and green pepper in the pan leftover from cooking the sausage. Cook until the onion is translucent and the peppers are softened. Transfer the vegetables into the slow cooker.
Rinse the split peas, transfer them into the slow cooker, then add the chicken stock, garlic, red pepper flakes, cayenne pepper, and salt. Stir to combine. The stock should cover the ingredients - if it does not, add more (or water) until it does.
Cook the soup on low for 6 to 8 hours.
Remove 2 cups of the soup and transfer it into a food processor. Process until smooth, then pour it back into the slow cooker. Stir to combine.
Add black pepper, additional salt, or red pepper flakes to taste. Top with croutons (or fresh bread on the side), then serve.