Bring a medium pot of water to a boil. Add the potatoes and boil until they're just starting to soften, then drain and set aside.
In a large pot, crumble and brown the Italian sausage with the onions over medium heat, about 5 minutes. Drain as much of the fat as you can (blotting the surface with paper towels helps). Add the chicken broth, milk, half-and-half, oregano and red pepper flakes to the pot with the sausage and onions, bring to a simmer and simmer for 30 minutes. Give it a taste and adjust the seasoning as needed with salt, pepper and more red pepper flakes if needed.
Add the potatoes and a splash of heavy cream for richness, then stir in the kale. Cover and simmer for an additional 10 minutes, then serve.