Place the potatoes in a Dutch oven and fill with enough water to cover. Bring to a boil; reduce heat to medium-low. Cover and simmer until potatoes are tender, and a fork can be easily inserted and removed, about 20 minutes. Drain and cool slightly. Peel, cut into cubes, and place in a large bowl.
To make the dressing, combine the tofu, lemon juice, mustard, garlic, and 1 teaspoon of salt in the bowl of a food processor. Blend until smooth. With the processor running, add the olive oil in a thin, steady stream, blending just until mixture thickens. Set aside.
Combine the celery, red bell pepper, eggs, green onions, and pickles in the bowl with the potatoes. Pour the dressing over the potato mixture, and toss lightly to evenly coat all ingredients. Season to taste with salt and pepper. Cover and chill at least 4 hours.
Just before serving, toss the salad with milk, 1 tablespoon at a time, to reach the desired consistency.