Bring a medium-sized pot of water to a boil on the stove. Crack each egg in its own bowl and set aside.
Add the vinegar to the boiling water. Stir the water to create a whirlpool effect. The circular motion helps the egg white gently wrap around the yolk once it’s dropped in the water.
Quickly add each egg to the spinning whirlpool of water, one after the other. Cover the pot with a lid, remove it from heat, and set a timer for 3 minutes.
When ready, pull the eggs out of the water with a slotted spoon. Set them on the paper towel lined plate and save the pot of water for the sauce. Use a pot lid to cover the eggs and keep them warm while preparing the sauce. The eggs will “reheat” when topped with hot hollandaise sauce, so it’s okay if they hang out until ready.
Mix together the salt, pepper and paprika and set aside. Create a double boiler over low heat with the water pot from the poached eggs.
Whisk together egg yolks and lemon juice in the double boiler. Keep the heat low while adding in 2 tbsp of butter at a time. Allow each chunk of butter to melt completely before adding more. This technique prevents the egg yolks from thickening too fast. The whole process takes only 1-2 minutes.
Stir the mixture until completely smooth. It will continue to set when removed from heat, so pull it off when the sauce has a consistency similar to pancake batter. If it thickens too quickly, whisk the thick sauce together with 1 tbsp of water over heat until the desired consistency is reached.
Don’t let the hollandaise sauce set. Quickly pour it over the poached eggs. Top with the salt, pepper and paprika seasoning to taste.