Combine the oil and butter in a medium saucepan and heat over medium-low heat until the butter is melted.
Add the garlic, oregano, pepper flakes, and a large pinch of salt and cook, stirring frequently, until fragrant but not browned, about 3 minutes.
Add the tomatoes, onion halves, basil sprigs, and sugar.
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.