Heat the olive oil in a large pot or deep skillet over medium heat.
Add the sliced chorizo and cook for 4-5 minutes until it releases its oils and starts to brown.
Add the chopped onion and cook for 3-4 minutes until softened and translucent.
Stir in the minced garlic, smoked paprika, and dried oregano; cook for 1 minute until fragrant.
Pour in the canned diced tomatoes with their juices, chicken broth, and season with salt and black pepper.
Add the dried penne pasta to the pot and stir to combine all ingredients.
Bring the mixture to a boil, then reduce heat to medium-low and simmer uncovered for 12-15 minutes, stirring occasionally, until the pasta is cooked and most of the liquid is absorbed.
Remove the pot from heat and stir in the grated Parmesan cheese until melted and well combined.
Taste and adjust seasoning with additional salt and pepper if needed.
Serve hot, garnished with chopped fresh parsley.