Dice the onions and bell pepper and sautee them in the olive oil over medium heat until they start to turn golden brown, about 10 minutes.
Add salt, black pepper, and sausage. Mix thoroughly with the onions and peppers. Continue sauteeing, breaking up any large chunks, until the sausage is cooked through and golden brown, another 15-20 minutes.
Add the Aleppo pepper flakes and garlic, stirring to combine. Let it sautee for another minute or two, just long enough for the garlic to start to get some color but before it burns.
Add the diced sweet potato and a little bit of the chicken broth. Scrape any brown bits (fond) off the pan to ensure the flavor is incorporated, and add the rest of the chicken broth. Bring to a low simmer.
Simmer at least an hour, until the sweet potato is very soft and all the flavors are well-incorporated. Near the end of the simmering stage, do a quick taste test and add extra salt, black pepper, or Aleppo pepper as needed.
A few minutes before serving, add the chopped kale and fresh herbs to the simmering pot. Leave it just long enough to wilt and get tender, about three minutes.
Just before serving, stir through the half and half and heat just long enough to bring it back to gently bubbling.