Place the eggs in a large pot. Fill the pot with water until the eggs are just covered.
Add the baking soda to the water and place the pot on the stove.
Turn the heat to medium-high and bring the water to a boil. (DO NOT add the eggs to boiling water.)
Once the water is boiling, turn off the heat and cover the pot. Let the eggs sit in the hot water for 12 minutes.
After the eggs have set, drain the hot water from the pot. Place the eggs in a colander and run under cold water to stop the cooking.
Transfer the eggs to a bowl or Tupperware container. Cover the container and refrigerate for 4 hours to overnight. (I recommend refrigerating the eggs overnight.)
Once the egg are chilled, tap the top and bottom of the egg against a hard surface to crack the shell. Usually, there is a resevoir/space at the bottom of the egg that will make it easy to start peeling off the shell. Remove all of the egg shells.
Use a sharp knife to cut the eggs in half longways so you end up with two symmetrical halves. Place the yolks in a mixing bowl and the whites on your deviled egg serving tray.
Use a fork to break up the egg yolks so they are in crumb-like pieces.
Add the mayonnaise, mustard, salt, and pepper to the egg yolks. Use a sturdy rubber spatula to smoosh everything together and smooth the eggs to create the smoothest filling you can. (You can also chop the yolks and mix the filling ingredients together in a food processor.)
Transfer the filling to a piping bag or a Ziploc bag with one corner cut off.
Pipe the egg yolk mixture into each of the egg white cavities, being sure to overfill each egg white.
Sprinkle the tops of the eggs with a little paprika.
Cover and store in the refrigerator until ready to serve.
The cooler the eggs are then easier they will be to peel. I would give the eggs at least 4 hours before trying to peel them. If the eggs need to cool more, the shell will stick to the eggs and cause the egg to tear or little pieces to rip off. You can keep going or wait for the eggs to cool longer. I've dealt with both situation over the years and cooking the eggs the day before is the easiest way to start this recipe.