Place the salted duck eggs in a small pot and cover with water. Bring it to a boil and then slightly reduce the heat and boil for another 10 minutes.
Rinse the eggs under cold water, then peel and discard the whites. Use a fork to mash the salted egg yolks finely, or use a spoon and press them against a sieve (mesh strainer).
Cut off about ¾ - 1 inch from the top tip of the shrimp heads with kitchen shears. Then cut off all the legs. You can also peel off the remaining shell around the head, but this is optional.
Use a sharp paring knife to make a slit down the back of the shrimp. Make sure not to cut all the way through. Remove any black veins.
Heat a generous amount of oil in a deep fry pan. White heating the oil, combine potato starch, all-purpose flour, baking powder and ⅛ teaspoon of salt in a shallow plate. Coat the shrimp generously with the flour mixture.
Once the oil reaches 375F (190C), add the shrimp and fry for 1-2 minutes until the shrimp are golden and just about cooked through. Deep fry in batches to avoid overcrowding the pan. Be careful not to overcook the shrimp. Drain and set aside.
Place a pan over medium heat, and add 1 tablespoon of oil to coat the bottom. Add minced garlic and sauté until fragrant.
Add the mashed salted egg yolk and the remaining salt. Stir and break up the egg yolk pieces and let it absorb the oil. Then lower the heat slightly and add the butter. Stir to melt the butter and form a creamy sauce.
Return the shrimp to the pan and toss quickly to coat them evenly with the sauce. Work quickly to avoid overcooking the shrimp and drying out the sauce. Transfer to a serving plate and serve right away.