Cook potatoes in large pot of boiling salted water until just tender, about 5 minutes. Drain potatoes; return to same pot. Place over very low heat just until excess moisture evaporates, about 1 minute. Transfer hot potatoes to large bowl; Cool 10 minutes(minimum). Mix in 2 cups mayonnaise, low fat variety optional.
Cook bacon in large heavy skillet over medium-high heat until brown and crisp. Transfer bacon to paper towels to drain. Cool bacon; crumble coarsely.
Mix remaining 1/2 cup mayonnaise, cheese, green onions, parsley and half of bacon into potatoes. Season salad to taste with salt and peper (I prefer a mixture of white and cayenne pepper and seasoning salt) Sprinkle with remaining bacon. (Can be made 2 hours ahead. Let stand at cool room temperature.).