Mash garlic and salt into a paste using a mortar and pestle; transfer to a food processor. Add roasted red peppers and 1 tablespoon oil; pulse just until a coarse puree forms. Transfer red pepper spread to a bowl and stir in basil, vinegar, sugar, and pepper.
Preheat oven to 350 degrees F (175 degrees C).
Brush both sides of bread slices with remaining 2 tablespoons oil. Arrange bread in a single layer on a baking sheet.
Bake bread slices in the preheated oven, turning once, until golden, about 25 minutes. Cool crostini on a rack.
Top each crostini with 3/4 tablespoon red pepper spread just before serving.