Place the potatoes in a large pot and cover with cold water by about 1 inch. Season the water generously with salt. Bring to a boil, reduce to a steady simmer, and cook for 12 to 15 minutes, or until very tender.
While the potatoes cook, hard-boil the eggs. Cool them in ice water, peel, and finely chop.
Drain the potatoes well, then return them to the warm pot for 2 to 3 minutes so excess moisture can evaporate.
Transfer the warm potatoes to a large bowl. Mash about two-thirds of the potatoes, leaving a few small pieces for texture.
Add the yellow mustard, pickle juice, kosher salt, black pepper, Cajun seasoning, and garlic powder while the potatoes are still warm. Mix gently.
Fold in the mayonnaise, chopped eggs, dill pickles, yellow onion, and green onions.
The potato salad should be thick, creamy, and scoopable. If it is too stiff, fold in 1 to 2 additional tablespoons of mayonnaise.
Taste and adjust with a little more mustard or salt if needed. Cover and refrigerate for at least 1 hour before serving.