Smash 3 of the cloves of garlic. Heat the oil in a large skillet over medium-high heat until hot. Add the onion, thyme and smashed garlic and cook until golden, about 6 minutes. Add the gin and cook until the liquid has reduced by half. Stir in the tomatoes with their juice, the olives and brine and bring to a simmer. Cook, stirring occasionally while breaking up the tomatoes, until the sauce is slightly thickened, 10 to 15 minutes. Season with 1/2 teaspoon salt and a couple turns of pepper.
Make 8 shallow wells in the sauce. Crack an egg into each and sprinkle with salt and pepper. Cover the skillet and simmer until the egg whites are set but the yolks are still runny, about 8 minutes.
Rub the toasted bread slices with the remaining 1 clove of garlic and serve with the eggs.
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