In a medium sized bowl, combine potatoes, bacon, cheese, basil, and pepper. Stir until well-blended, about 1 minute.
In a tall-walled medium-sized pot, warm oil on medium high heat for 10 minutes.
Meanwhile, lay wonton wrappers on a flat surface. To fill each envelop, Place 1 TBSP of filling on one corner of each wrapper. Roll same corner (filling inside) halfway toward far corner. Fold left and right corners of wrapper over filling. Finally, roll wrapper the rest of the way to far corner. Using your finger, brush a dime size bit of water inside the final corner. Place envelopes (final corner side down) on a flat surface.
Line a plate with a paper towel (to drain excess oil after puffs are cooked).
In a small bowl, combine all six dipping sauce ingredients and set aside.
Gently place 4-5 envelopes in hot oil at a time. Fry until golden brown, 1-2 minutes, flipping once. If final flap begins to lift from envelope, gently press back down with slotted spoon. Remove envelopes from oil with slotted spoon and place on paper towel-lined plate. Transfer to another plate, sprinkle with remaining green onion as garnish, and serve with dipping sauce.
Note: Fully-cooked envelopes can be frozen and re-heated in the oven at 350 degrees for 12-15 minutes, turning every 5 minutes. Makes a great make-ahead party food!