Hard boil your eggs and remove the shells. (For perfect hard-boiled eggs, I use this method.) Set the eggs 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 (that 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 I let mine sit about 16 hours.

When brining time is finished, remove the eggs from the brine. Cut each egg in half from top to bottom. Scoop out the yolks and place in a medium bowl. 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.

Use a spatula to scoop all the filling into a resealable sandwich bag or piping bag fitted with a ½-inch round tip. Press the bag with your hands to push all the filling to one corner and press any air out of the top. If using a plastic bag, snip one corner off with a pair of scissors.

Pipe the filling into the cup of each egg white, filling the cups so that the filling mounds a little over the top. Squeeze the bag from the top to force the filling downward. (Alternatively, scoop the filling into the egg whites with a spoon.) Sprinkle with chopped rosemary and season with salt and pepper.