Place eggs in a pot, cover with cold water by 1 inch, and bring to a boil. Cover, remove from heat, and let sit 12 to 15 minutes.
Transfer eggs to an ice bath until completely cool, about 10 minutes, then peel.
Cook elbow macaroni according to package directions. Drain and rinse under cold water until cool.
Chop eggs into rough chunks.
In a very large bowl, stir together mayonnaise, yellow mustard, white vinegar, and dill relish until smooth.
Add cooled pasta and stir to coat. Fold in chopped eggs gently. Season with salt and pepper.
Cover and refrigerate at least 2 hours. Stir before serving, adjust seasoning, and sprinkle generously with paprika.
Notes
Cool both the pasta and eggs completely before mixing so the mayonnaise stays smooth. Use yellow mustard rather than Dijon for the classic deviled egg flavor. Chill for at least 2 hours so the pasta absorbs the dressing. Taste again before serving because cold salad often needs another pinch of salt.