Hard boil your eggs and remove the shells then set aside.
To prepare the brine, pour a can of pickled beets into a large bowl. Add the cider vinegar, sugar, peppercorns, and salt, and stir to combine. Carefully (because beet juice will stain) place the peeled eggs into the brine. Cover and refrigerate for at least 12 hours or up to 3 days. The longer you leave them in the brine, the more sour and pink they'll end up. I like just the rim of pink and slight pickled flavor, so let them sit about 16 hours.
When brining is finished, remove the eggs from the brine and cut each egg in half.
Scoop out the yolks and place in a medium bowl then add the olive oil, mayonnaise, white vinegar, mustard, and curry powder. Mix and mash with a fork until smooth. Add a little bit of water to the mixture if it's too stiff. Taste and season with salt and pepper as needed.
Scoop all the filling into a resealable sandwich bag or piping bag fitted with a 1/2-inch round tip.
Pipe the filling into the cup of each egg white or scoop the filling into the egg whites with a spoon and sprinkle with chopped rosemary and enjoy!