In a food processor, combine half of the tomatoes, all of the garlic, coarsely chopped pepper, bread, vinegar, salt, cumin, and sugar.
Process until smooth.
With the motor running, gradually add the remaining tomatoes and blend until smooth.
Slowly drizzle in the olive oil until fully incorporated.
Strain the mixture through a fine-mesh strainer into a medium bowl, pressing with the back of a ladle to extract as much liquid as possible.
Discard the solids.
Cover the bowl and refrigerate the gazpacho for at least 2 hours, or overnight, to chill and allow the flavors to meld.
Before serving, taste the gazpacho and adjust the seasoning with more vinegar or salt if needed.
If the soup is too thick, you can thin it with a bit of ice water.
Pour the chilled gazpacho into individual bowls and garnish with finely chopped red and green bell peppers, if desired.