Throw the strawberries, tomatoes, basil, cucumber, bell pepper and garlic into a food processor with 1/2 teaspoon salt and pulse until you have a coarse puree. Taste, add the vinegar, some oregano and more salt if needed and chill until ready to serve.
Brush a griddle pan with olive oil and grill the bread until toasted.
Serve the gazpacho cold. Garnish with a drizzle of olive oil, some torn basil and the grilled bread on the side.