Peel and cut both russet and yukon gold potatoes into 1-inch chunks, keeping them in a bowl of cold water to prevent discoloration. Finely dice the celery into 1/4-inch pieces and finely chop the gherkin pickles for consistent texture. Having everything prepped and ready will make the cooking process smooth and efficient.
In a small pot, whisk together the milk and corn starch until smooth, then place over high heat. Once it begins to boil, stir in the Dijon mustard, brown sugar, salt, onion powder, and garlic powder, continuing to stir until the mixture thickens—about 2-3 minutes. Lightly temper the beaten egg by mixing 1 teaspoon of the hot sauce into it, then slowly stir the egg mixture back into the pot, whisking constantly until the sauce reaches 135°F and coats the back of a spoon. I like to use a thermometer here to ensure the egg is safely cooked without scrambling.
Drain the prepared potatoes and add them to a clean pot with the water, salt, vinegar, and sweet pickle juice. Stir gently to combine, then place the 3 whole eggs directly on top of the potatoes (don't stir them in). Cover and pressure cook on high for 1 minute, then allow 5 minutes of natural pressure release before carefully releasing any remaining pressure. Transfer the eggs to an ice water bath to cool and stop the cooking process.
While the potatoes are still warm, transfer them to a large bowl and pour the cooked dressing from Step 2 over them, stirring gently to coat evenly. Fold in the mayonnaise until well combined, then add the diced celery and chopped pickles from Step 1, mixing carefully to maintain the potato chunks. Peel and chop the cooled hard-boiled eggs and fold them into the salad. I prefer to add the eggs just before chilling so they stay a bit firmer rather than absorbing too much moisture.
Transfer the assembled potato salad to a serving bowl and refrigerate for at least 4 hours (or up to overnight) to allow the flavors to meld and the salad to chill thoroughly. Give it a gentle stir before serving, adding a pinch of paprika on top for a traditional Amish touch if desired.