First and foremost, this recipe is adaptable to your tastes. Feel free to increase or decrease amounts and play around with it. The ingredient amounts listed seem to be a good balance of flavor, but I understand preferences, too.
Place about 2” of water in a medium saucepot. Place the steamer basket into the pot and place the lid on the pot. (Use more or less water so that there is about an inch of space between the steamer basket and the top of the water.)
Bring the water up to a boil, then lower the heat to a gentle simmer. Remove the lid and carefully place the eggs into the basket. You may use a slotted spoon to carefully transfer them; there will be steam coming from a hot pot.
Place the lid back onto the pot and steam for 13 minutes for a slightly jammy center, or 14 minutes for a more fully cooked yolk.
While the eggs are steaming, add ice cubes and cold water to a medium bowl. Set it in the refrigerator until ready to use.
Just before the eggs have finished steaming, pull the ice bath from the refrigerator.
When the timer is finished for steaming, carefully, remove the eggs, one by one, with a slotted spoon or spider strainer and place the eggs into the ice bath.
Let the eggs sit in the ice bath for at least 20 minutes. Add more ice as needed so the water stays very cold.
After the ice bath has chilled the eggs, you may continue with the recipe, or remove them to a small bowl and refrigerate for up to 3 days.
Gently tap an egg on the counter or cutting board to crack the shell on all sides. Begin to peel the shell and thin membrane away from the hard-boiled egg. Run the egg under water to remove any minute fragments of shell. Place the peeled egg onto a plate or shallow bowl. Continue with the remaining eggs.
Cut each egg in half longways, scooping out the yolks into a medium bowl. Place the egg whites on a plate or platter.
Add the tomato paste, mayonnaise, white pepper, paprika, salt, and vinegar to the egg yolks. Use a fork or meat masher to blend the mixture together well. Switching to a silicone spatula helps in the final mixing.
Taste and adjust any seasoning as desired, combining them well.
You may scoop by tablespoonfuls of the filling mixture to fill the egg whites, or you may use a piping bag with a tip to fill them. (I would not use a closed star tip, but something with a big enough opening in case there are chunks of egg yolks that could clog the tip.)
Once all the eggs have been filled, lightly sprinkle with extra ground white pepper and/or paprika.
Serve or cover well (without mashing the tops down) and refrigerate for up to a week. (FDA says, "Use or eat hard-cooked eggs (in the shell or peeled) within 1 week after cooking.)