Warm the olive oil in a large deep skillet or pot over medium heat.
Sauté the onion until translucent, about 3 to 4 minutes.
Add the ground beef and a pinch of salt. Cook, crumbling, until no pink remains. Drain excess fat.
Stir in garlic, tomato paste, Italian seasoning, paprika, and red pepper. Cook 1 minute, stirring.
Pour in marinara and broth. Scrape up browned bits and bring to a lively simmer.
Stir in dry pasta shells. Reduce heat, cover, and cook 10 to 12 minutes, stirring occasionally.
Uncover and stir in heavy cream, remaining salt, and black pepper. Simmer 2 minutes to thicken.
Fold in mozzarella and half the Parmesan until melted. Rest 2 minutes, then garnish with parsley and remaining Parmesan.