Add the linguine, whole tomatoes with their juices, sliced garlic, broth, olive oil, red pepper flakes, and salt to a large, deep skillet or pot.
Use a wooden spoon to break up the whole tomatoes into smaller pieces right in the pot.
Bring everything to a boil over high heat, then reduce to a steady simmer.
Cook for 12-15 minutes, stirring and tossing the pasta every 2-3 minutes to prevent sticking, until the pasta is al dente and the liquid has reduced to a silky sauce.
Remove from heat and stir in the torn basil leaves.
Serve immediately topped with grated Parmesan cheese and additional basil if desired.