Pour the tomatoes and juice into a strainer set over a large bowl. Using your hands, open up the tomatoes and remove and discard any fibrous cores. Let the tomatoes drain any excess liquid, about 5 minutes.
Remove 3/4 cup of the tomatoes from the strainer and set aside. Reserve 2 1/2 cups of the tomato juice and discard the remainder.
Heat the olive oil in a 12 inch skillet over medium heat until shimmering. Add the onion and cook, stirring occasionally, until softened and golden around edges, 6 to 8 minutes. Add the garlic and oregano and cook, stirring constantly, until the garlic is fragrant, about 30 seconds.
Add the tomatoes from the strainer and cook over medium-high heat, stirring frequently, until the liquid has evaporated and the tomatoes begin to stick to the bottom of the pan and brown fond forms around the pan edges, 10 to 12 minutes.
Add the wine and cook until thick and syrupy, about 1 minute. Add the reserved tomato juice and simmer over medium heat, stirring occasionally and loosening any browned bits, until the sauce is thick, 8 to 10 minutes.
Pulse the sauce and the reserved tomatoes in a food processor until slightly chunky, about eight 2-second pulses. Return the sauce to the skillet and add the basil and extra-virgin oil. Season with salt, pepper, and sugar to taste.
This sauce can be refrigerated in an airtight container for 4 days, or frozen for up to 2 months.