Cook potatoes in large pot of boiling salted water until just tender. Drain and cool. Cut potatoes into 3/4-inch pieces. Transfer to large bowl.
Cook bacon in heavy large skillet over medium heat until brown and crisp, stirring occasionally. Using slotted spoon, transfer bacon to paper towels and drain. Mix mayonnaise, mustard, chopped thyme, allspice, turmeric and cayenne pepper in medium bowl.
Separate egg yolks and whites. Mash yolks in small bowl. Mince egg whites. Add bacon, mayonnaise mixture, yolks, whites, cornichons, celery, onion and hot pepper sauce to potatoes in bowl and toss to coat. Season to taste with salt and pepper. Sprinkle with parsley. (Can be prepared 1 day ahead. Cover and refrigerate.).