Preheat the oven to 375 degrees F. Heat 1 1/2 tablespoons olive oil in a large ovenproof skillet over medium-high heat. Add the onion and cook, stirring, until golden, about 5 minutes. Add the tomato paste and cook, stirring, 1 more minute. Stir in the vinegar, honey mustard, Worcestershire sauce, 1/2 cup water, and salt and pepper to taste. Bring to a simmer, then add the beans, plus the liquid from one of the cans. Cook until the beans are soft, about 5 more minutes.
Make eight indentations in the bean mixture and crack an egg into each. Sprinkle with salt and pepper and transfer to the oven. Bake until the egg whites are set, 10 to 14 minutes.
Meanwhile, heat a large skillet over medium-high heat. Brush the bread with olive oil on both sides and toast in the skillet, 1 minute per side. Toss the tomatoes, parsley, the remaining 1/2 tablespoon olive oil, and salt and pepper to taste in a bowl. Divide the toast among plates; top each with 2 eggs, some beans and the tomato salad.