Pasta in butter tomato sauce - Test 2

https://cooking.nytimes.com/recipes/1022464-tomato-butter-pasta

1 - Weird. I'm sure I've made this once before. If I did, I took no notes. This was incredibly quick and very easy. It's important to have good, flavorful tomatoes - the winter grocery store tomatoes or, as my dad called them "Canadian Tire tomatoes", just won't do, since the flavor all comes from the fresh tomato. I don't know if the butter needs to be frozen and grated. The noodles go back into the pot hot and then you cook the sauce, so in chunks should be plenty fine. Also, how about undercooking the noodles before draining them and then finishing them in the tomato? Sort of just pre-al-dente? Or would that cook the tomato too much?

2 - How long has it been since I've had good vine-ripened tomatoes? I celebrated our first ripe tomatoes with this recipe. I think it is quite simple, I just need to adjust a few things.

3 - I forgot the basil. How could I forget the basil?!? It was still good but was missing something. The interesting bit was the sauce. I thought there would be too much, but cooking the pasta in the sauce flavors the noodles and reduces the sauce.

4 - This is a good quick recipe when you have glut of tomatoes. It's like Ben's herbed buttered pasta in that it's quick and easy.

1lb pasta (any kind, linguine prefered)

2lbs large, ripe tomatoes, cut in half horizontally

¼ cup (2oz/58gr)  frozen butter (try cutting in chunks instead of freezing and grating it)

1 large garlic clove, peeled

¼ tsp red-pepper flakes, plus more for serving

1/2 tsp? salt 

¼ tsp? black pepper

Finely sliced basil leaves, for serving

Finely grated Parmesan, for serving

1. Cook the pasta in plenty of salted water. Reserve 1 cup pasta cooking water.
2. Meanwhile, using the large holes of a box grater, grate the cut ends of the tomato into a large bowl. Compost skins. 
3. Grate the butter into the bowl as well. 
4. Finely grate the garlic into the bowl as well, then add the red-pepper flakes.
5. Season generously with salt. Refrigerate until ready to use.
6. Drain the pasta and replace with the grated tomato mixture. Bring to a slow boil before returning the drained pasta to the pot. 
7. Set over medium-high heat and cook, stirring constantly, until the mixture thickens slightly and glosses the pasta, 2 to 3 minutes (the sauce will continue to thicken as it sits). 
8. If you want a thinner sauce, add pasta water as needed to emulsify the sauce. 
9. Adjust the seasoning to taste with salt and pepper. 
10. Serve with more red-pepper flakes, black pepper, basil and Parmesan as desired.