Create a flavorful tomato sauce: Heat olive oil in a saucepan, sauté onion and garlic until soft for 12-15 minutes. Crush tomatoes in their liquid, stir in tomato paste and sugar for a rich, well-combined sauce.
Bring the sauce to a boil, then simmer over medium-low heat, uncovered, stirring often, for 25-30 minutes until thickened and all the liquid evaporates. Season with salt, pepper, and a touch more sugar if needed. Allow to cool.
In a large saucepan over medium heat, heat oil. Add brown onion, garlic, and chillies and cook for 3 minutes until very soft. Transfer to a large bowl and mix in tomato sauce, tomato juice, salt, and pepper. Cover with plastic wrap and refrigerate overnight.
Garnish cold soup with fresh coriander, diced onion, crispy croutons, sliced cucumber, and a dollop of sour cream.