2 (28-ounce) cans whole peeled tomatoes (about 1.5kg total) (see note above)
2 tablespoons (30ml) extra-virgin olive oil, plus more for finishing
2 tablespoons (30g) unsalted butter
4 cloves garlic, minced
1/2 teaspoon (about 2g) red pepper flakes
1/2 tablespoon (about 4g) dried oregano
1 small carrot (about 4 ounces; 110g), cut into large chunks
1 small onion (about 5 ounces; 140g), split in half
1 large stem fresh basil
Kosher salt and freshly ground black pepper
2 teaspoons (10ml) Asian fish sauce, optional
1/4 cup (about 10g) minced fresh parsley or basil leaves (or a mix of the two)
Place tomatoes in a large bowl. Using your hands, crush tomatoes by squeezing them through your fingers until pieces no larger than 1/2 inch remain. Transfer 1 cup (240ml) of crushed tomatoes to a sealed container and reserve in the refrigerator until step 3.
Heat olive oil and butter over medium heat in a pressure cooker until butter is melted. Add garlic and cook, stirring, until softened and fragrant but not browned, about 2 minutes. Add pepper flakes and oregano and cook, stirring, until fragrant, about 1 minute. Add tomatoes, carrot, onion, and basil and stir to combine. Season lightly with salt and pepper. Seal pressure cooker and bring to high pressure. Cook for 45 minutes, then release pressure and open lid.
Using tongs, discard onion halves, carrot, and basil. Add reserved tomatoes to sauce and stir to combine. Add fish sauce, if using. Season generously with salt and pepper and stir in minced herbs, along with additional olive oil as desired. Serve immediately, or allow to cool at room temperature, transfer to airtight containers, and refrigerate for up to 1 week. Sauce can also be frozen in sealed containers for up to 6 months. To reheat, warm very gently in a saucepan with 1/2 cup (120ml) water, stirring until it all melts and heats through.