Make soup: Warm olive oil in a large pan over medium-high heat. Add onion and cook, stirring, until softened, 5 minutes. Stir in thyme; cook 1 minute. Add tomatoes and broth. Bring to a simmer and cook, uncovered, until tomatoes are softened and soup is slightly thickened, 25 to 30 minutes. Season with salt and pepper.
Remove from heat and cool slightly. Puree in a blender or food processor. Pour into a bowl, cover and chill at least 6 hours or overnight.
Make croutons: Preheat broiler to high and set a rack about 8 inches from heat source. Brush both sides of bread with butter and place on a baking sheet. Broil, watching carefully to prevent burning, until golden brown, about 3 minutes per side.
Rub each crouton with halved garlic while warm. Arrange 3 croutons on top of each bowl of soup or 1 crouton in a cup of soup, or serve alongside.
