Preheat the oven to 350 degrees.

Season the short ribs generously with salt and pepper on all sides.

Heat the vegetable oil in a Dutch oven or large covered casserole dish over medium-high heat. Working in batches, brown the short ribs on all sides. Remove from the pot and transfer to a bowl or plate.

Add the chorizo, onion, and carrots and cook, stirring occasionally, until the onions are translucent, about 5 minutes. Add 3 garlic cloves and cook, stirring, for 30 seconds. Add the tomato paste and cook, stirring, for another 1-2 minutes. Add the wine and cook until reduced by half. Add the ribs back to the pot. Pour in 2 cups beef broth and add the canned tomatoes and bay leaves. Bring to a simmer, cover the pot, and transfer to the oven. Cook until the meat is very tender, about 3 hours.

Remove the pot from the oven and as soon as the meat is cool enough to handle, remove the meat from the bones. Discard the bones, any large pieces of fat, and the bay leaves. Let cool, then refrigerate, covered, overnight or for up to 2 days.

Before serving, remove the pot from the oven and skim off any fat that has hardened on top. Place on the stove over medium heat, add the remaining ½ cup beef broth, and bring to a simmer over medium heat.

Bring a large pot of salted water to a boil and cook the penne according to the package directions. Drain.

Stir the drained pasta into the sauce and serve with the parsley mixture on top.