Soak beans in a pot of water for 8 hours to overnight. Bring to a boil; cook on medium heat until soft, about 1 hour. Divide beans between 3 bowls; mix in tomatoes.
Preheat the oven to 350 degrees F (175 degrees C). Place onions on a baking sheet.
Bake in the preheated oven for 25 minutes.
Place 2 tablespoons of cooked beans in a bowl and crush into a pulp. Mix in oil, vinegar, tahini, garlic, salt, and pepper. Pour dressing over the beans and tomatoes. Mix well. Decorate with eggs and a pile of parsley on top. Serve piyaz at room temperature with lemon slices and baked onion, or place a bite of piyaz into a sweet onion ‘boat’ to bring out the flavor. Squeeze lemon juice on top.