Heat the olive oil in your pot over medium heat, then add the sausage and break it into crumbles as it cooks. Let it brown for about 4 to 5 minutes until it's no longer pink in the middle. Pull it out and set it on a plate, leaving the flavorful bits behind in the pot.
Add the chopped onion to the same pot and cook until it turns soft and translucent, roughly 4 minutes. Stir in the diced sweet potato and garlic, cooking for another 3 minutes so the potato starts to soften. This step is where most of the dish's flavor base comes together.
Pour in the pasta, chicken broth, diced tomatoes, and tomato paste, then stir in the Italian seasoning and red pepper flakes. Make sure the pasta is mostly submerged in liquid so it cooks evenly. Bring everything up to a boil before dropping the heat down.
Reduce the heat to medium-low, cover the pot, and let it simmer for about 12 to 15 minutes. Stir occasionally so the pasta doesn't stick to the bottom of the pot. You'll know it's ready when the pasta is al dente and most of the liquid has absorbed into a thick sauce.
Add the baby kale in batches, stirring until each handful wilts down before adding more. Return the cooked sausage to the pot and stir everything together until it's heated through. Let the pot sit off the heat for 5 minutes so the sauce thickens slightly.
Sprinkle the lemon zest and grated Parmesan over the top right before serving. The lemon cuts through the richness and makes the whole dish taste brighter. Give it one last gentle stir so the cheese starts to melt into the hot pasta.