In a large, wide pan place the linguine and fill with enough water to just cover.
Add salt to the water til it tastes salty.
Bring to a boil over high heat. Stir frequently, so pasta doesn't stick.
Once you reach a boil stir again, and reduce to a simmer. Put a lid on over the pot.
When the pasta is al dente, remove the pasta with tongs and place on a plate or bowl. Don't dump the water, pour it out into a bowl and set aside.
Add the tomato sauce to the pan. Heat up over medium heat. Add a little bit of the pasta water (if necessary) at a time to keep the sauce from burning or becoming too thick.
Once the sauce is hot, doesn't need to be boiling, add in the spinach/kale/chard, fresh basil, and halves cherry tomatoes. Simmer until the greens have wilted.
Stir in ¼ cup of heavy cream. Add the linguine back in. Toss with tongs to coat. Serve.