Smash and peel 3 garlic cloves.
Heat 2 tablespoons olive oil in a large saucepan over medium heat until shimmering. Add the garlic and sauté until fragrant and pale golden, 1 to 2 minutes.
Carefully pour in 1 (28-ounce) can whole peeled tomatoes and their juices. Add 1 large fresh basil sprig, if using, season with 1 teaspoon kosher salt and 1/4 teaspoon black pepper, and stir to combine. Bring to a boil.
Reduce the heat to medium-low and simmer uncovered until the sauce is slightly thickened, carefully breaking the tomatoes up a bit with a wooden spoon as they soften, about 20 minutes.
Remove the saucepan from the heat. Remove and discard the basil sprig.
Blend with an immersion blender directly in the pan until completely smooth. (Alternatively, transfer the mixture to a stand blender and blend until completely smooth.)
Taste and season with more kosher salt and black pepper as needed.