Pour the canned whole peeled tomatoes into a fine-mesh strainer set over a bowl and let drain for 5 minutes; reserve the strained juice.
Transfer the drained contents to a bowl and crush firmly by hand until mostly smooth with small pieces, 1–2 minutes, or pass through a food mill for a smoother texture.
Stir in the fine sea salt and the extra-virgin olive oil until evenly combined.
Fold in the torn fresh basil leaves.
Adjust consistency with a little reserved juice at a time until the sauce is thick and spoonable, not watery.
Let rest at room temperature for 15–30 minutes so the flavors meld.
Use about 1/4 cup per 12-inch pizza, spreading in a thin, even layer; refrigerate leftovers in an airtight container for up to 3 days.