Preheat oven to 425°.
To prepare soup, arrange tomatoes, cut sides up, 2 garlic cloves, onion slices, and bell pepper half on a jelly-roll pan coated with cooking spray. Bake at 425° for 1 hour and 10 minutes or until golden. Cool. Chop tomatoes, onion, and bell pepper. Set 1/3 cup chopped onion aside for the toasts. Squeeze garlic cloves to extract pulp; discard skins.
Heat olive oil in a Dutch oven over medium heat. Add remaining chopped onion, bell pepper, cumin, and coriander; cook 5 minutes, stirring frequently. Add harissa and paprika; cook 2 minutes. Stir in tomatoes, garlic pulp, broth, water, and 1/2 teaspoon thyme; bring to a boil. Cover, reduce heat, and simmer 15 minutes. Remove from heat; let stand 5 minutes. Stir in lemon juice, salt, and black pepper. Place one-half of tomato mixture in a blender, and process until smooth. Pour into a bowl. Repeat procedure with remaining tomato mixture.
To prepare toasts, rub cut sides of the halved garlic clove over one side of each bread slice. Combine reserved 1/3 cup chopped onion, olives, parsley, vinegar, and 1/8 teaspoon thyme. Top each bread slice with about 1 tablespoon olive mixture. Ladle about 1/2 cup soup into each of 8 bowls. Top each serving with 1 teaspoon yogurt; serve with 1 olive toast.