To a heat safe bowl or the top of a double boiler add two egg yolks. (Discard the egg white part.) Also add the half and half, lemon juice, salt and Dijon mustard. Whisk the ingredients together.
Bring 2 inches of water to a boil in a saucepan, or the bottom pan of the double boiler. Reduce the heat to a simmer then place the hollandaise bowl on top of the saucepan. Continuously whisk the hollandaise sauce for 5 minutes.
In a small bowl add the cornstarch and water, stir together. Add the cornstarch mixture to the hollandaise sauce. Continue to whisk the mixture for 5 minutes or until the sauce has thickened.
To poach the eggs, bring a large pot of water to a boil. Add a teaspoon of salt and a tablespoon of vinegar to the water (optional).
Once the water is boiling, use a spoon to stir it in a circular motion, creating a swirling vortex. Add one egg to the center of the boiling water and let it cook for 3 minutes. Use a slotted spoon to remove the egg from the water. Repeat with the remaining eggs.
Toast the English muffins and ad them to a plate. Add one slice of Canadian bacon to each muffin half.
Top the Canadian bacon with a poached egg.
Add a spoonful of the hollandaise sauce to each of the muffins. If the hollandaise sauce gets too thick before adding it, mix in a tablespoon of water and whisk until smooth.
Top each English muffin with smoked paprika and chives.