Process tomatoes (1 can) and their juice through food mill, pulse in food processor until puréed, or purée with immersion blender. Purée should not be completely smooth, but should have no chunks larger than 1/16th of an inch. Set tomatoes aside.
Combine extra-virgin olive oil (1 tbsp) and unsalted butter (1 tbsp) in medium saucepan and heat over medium-low heat until butter is melted. Add grated garlic (2 cloves), dried oregano (1 tsp), red pepper flakes (pinch), and a large pinch of salt (some) and cook, stirring frequently, until fragrant but not browned, about 3 minutes. Add tomatoes, yellow onions (2 halves), basil (2 sprigs), and sugar (1 tsp). Bring to a simmer, reduce heat to lowest setting (bubbles should barely be breaking the surface), and cook, stirring occasionally, until reduced by half, about 1 hour. Discard onions and basil stems. Season to taste with salt. Allow to cool and store in covered container in the refrigerator for up to 2 weeks.