In a large nonstick skillet, heat olive oil over medium-high heat. Add garlic and cook, stirring, until garlic begins to brown lightly. Add basil and tomatoes, breaking up tomatoes with the back of a spoon; season with salt and pepper.
Bring sauce to a boil and immediately remove from heat. Strain sauce through a coarse mesh sieve into a large bowl, pressing down on solids. Discard solids.
Return sauce to skillet. Bring to a boil and immediately reduce heat to a simmer. Let simmer until slightly thickened, about 5 minutes. Use immediately or keep refrigerated, up to 1 week.