Dry the pork well and sprinkle it on all sides with 1 tablespoon of the kosher salt and the pepper. Heat 2 tablespoons of the vegetable oil in a Dutch oven over high heat. Working in batches to avoid crowding the pan, brown the pork on all sides, about 4 minutes per side. Remove the pork to a plate and set aside. While the pork is browning, tie the thyme, rosemary and bay leaf into a bundle using butcher's twine.
Once all of the pork has been browned, reduce the heat to medium. Add the remaining 1 tablespoon vegetable oil no oil remains in the pot. Add the onions and the remaining 1/2 tablespoon kosher salt. Cook for about 8 minutes, stirring and scraping up any browned bits. Add the garlic and cook for another 2 or 3 minutes. Deglaze with the white wine and cook until reduced to nearly dry, 6 to 10 minutes. Add the chicken broth, crushed tomatoes, Parmesan rind, chile flakes and the herb bundle and bring to a simmer. Return the pork to the pot, tucking it in under the sauce. Reduce the heat to low and simmer, covered, until the pork is fork tender, about 1 hour 45 minutes.
Remove the pork and shred into bite-size pieces using two forks. Remove the herb bundle from the sauce and add the pork back to the pot. Stir in the olive oil and half of the grated Parmesan. Keep warm over low heat.
Bring a large pot of salted water to a boil and cook the penne for about 1 or 2 minutes less than the package directions. Drain and add the pasta to the sauce, tossing to coat. Finish cooking the pasta in the sauce, about 2 minutes, adding a ladle of pasta water as needed. Serve topped with the remaining grated Parmesan, or more as desired, and a drizzle of olive oil. Garnish with a few leaves of baby arugula, if using.
Recipe courtesy of Giada De Laurentiis