Place salt, tomatoes, garlic, bread, and onion in a bowl, cover with boiling water, and let sit for 1 hour. Drain vegetables, reserving 1 cup soaking liquid; place in blender. Squeeze water from bread; place in blender with reserved soaking liquid, oil, and vinegar. Purée until smooth; season with salt and pepper, and chill. Pour into serving bowls; top with eggs, ham, and a drizzle of oil.