Heat the oil and garlic together in a small skillet over medium-low heat just until the oil is warm and the garlic is soft, about 5 minutes.
Remove skillet from the heat and let set to infuse the oil, about 30 minutes.
Pour fresh tomatoes and their juices into a bowl.
Squeeze the tomatoes through your fingers until the are coarsely crushed.
Stir in the garlic in its oil and the basil.
Season with salt and pepper.
Let stand for 1 to 2 hours for the flavors to marry.
Bring a large pot of water to a boil over high heat (with 1 Tbsp. salt added if preferred).
Add the pasta and stir well, separating the strands.
Cook according to the manufacturer’s directions until al dente.
Drain well.
Return the tagliarini to its cooking pot.
Add the sauce and mix well.
Add salt and pepper to taste.
If you feel it is slightly bitter, add a little bit of sugar at a time until the flavor is more balanced and to your preference level.
Cover and let rest for a minute.
Serve hot.