Place the eggs into a pot in a single layer and add enough water to cover them by an inch. Place the pot on the stove top and bring to a boil. Once boiling, turn of the heat, place a lid on the pot and let sit for 10 minutes. After 10 minutes remove the eggs into an ice bath and, while eggs are still slightly warm, crack the eggs and peel off the shell. Place the peeled eggs into one 64-ounce glass jar or two 36-ounce glass jars.
Strain the beets from the liquid in the jar, reserving both. Add the beets into the jar on top of the eggs. This will help keep the eggs submerged in the liquid. Put the beet liquid into a sauce pot with 1 cup of water, white vinegar, sugar and salt. Bring to a boil. Once boiling, pour the liquid into the jar to cover the eggs and beets. Place a lid on the jar and refrigerate for at least 12 hours before serving.
The pickled eggs can be made a week in advance.
Cut the eggs in half, lengthwise. Remove the yolks to the bowl of a food processor and place the eggs onto a serving tray.
To the food processor bowl with the yolks, add mayo, Dijon mustard, vinegar, prepared horseradish, salt, cayenne and capers. Puree the mixture until smooth, scraping down the sides of the halfway through. Once smooth, add the dill and chives and pulse just until combined.
Put the filling into a piping bag or zip top bag. Snip the piping bag or zip top bag and squeeze the filling into the eggs. Top each with a small piece of smoked salmon and a garnish of some chives and dill.
Grant Melton is an Emmy Award-Winning Producer of the Rachael Ray Show, food writer and recipe developer. He's a contributor to Food52, Food Network Kitchen and Rachael Ray Every Day Magazine. He loves cookies, cocktails and kindness.