Prepare the lime water: combine juice of 1 lime with 2 cups cold water in a medium bowl. Peel and cube the apples into ½-inch pieces and place immediately into the lime water. They will sit here while you prepare everything else. The lime water prevents browning and keeps the apple firm and bright.
Cook the vegetables: bring a large pot of salted water to a boil. Add diced potatoes and carrots together. Cook 12-15 minutes until tender when pierced with a fork but still holding their shape. Drain and spread on a sheet pan to cool completely - minimum 30 minutes. Do not dress warm vegetables.
Hard-boil the eggs: place eggs in a single layer in a saucepan, cover with cold water by 1 inch. Bring to a boil, reduce heat to a gentle simmer, cook exactly 10 minutes. Transfer to an ice bath immediately for 5 minutes. Peel and separate - yolks go into a bowl for the dressing, whites go onto a cutting board to be cubed.
Make the egg yolk dressing: place the 4 yolks in a medium bowl. Using a fork, mash them thoroughly until no lumps remain - they should be smooth and powdery. Add the grated onion, avocado oil mayo, apple cider vinegar, and salt. Mash and stir everything together until the dressing is smooth, creamy, and uniform. Taste and adjust salt. If the dressing seems too loose, add 1 tablespoon softened cream cheese and stir until fully incorporated. Refrigerate until ready to assemble.
Cube the egg whites: cut the boiled egg whites into ½-inch pieces, same size as the potato and apple dice. Set aside.
Drain the apples: remove the apple cubes from the lime water and pat completely dry with paper towels. Any excess lime water will thin the dressing.
Assemble: in a large bowl combine the fully cooled potatoes, carrots, drained apple cubes, cubed egg whites, and drained sweet corn. Pour the egg yolk dressing over and fold gently with a wide spatula until everything is evenly and thoroughly coated. The dressing should cling to every piece - not pool at the bottom. Taste and adjust salt.
Chill: transfer to a serving bowl or platter. Press plastic wrap directly onto the surface of the salad. Refrigerate minimum 2 hours, overnight preferred.
Decorate at the table: just before serving, arrange the canned white asparagus spears across the top of the salad. Scatter petit pois over the surface. Serve cold directly from the refrigerator.