In a small saucepan, melt the butter over low heat. In a small bowl, using a whisk, beat the egg yolks until creamy. Blend in the lime juice, heavy whipping cream, salt, and pepper.
Once the butter has melted in the saucepan, take a tablespoon of the hot butter and pour it into the egg mixture. Blend well, adding a tablespoon of butter at a time until all the butter has been incorporated into the egg mixture.
Once the melted butter and egg mixture are blended, return the mixture to the saucepan. Cook the sauce on low heat, continually stirring it, for about 30 seconds. Remove the saucepan from the heat and set it aside.
Next, fill a medium saucepan with 4 inches of water. Bring the water to a boil and then reduce the water to a simmer. Add the vinegar to the water. (The vinegar will help tighten the egg whites and achieve a spherical shape.)
While waiting for the water to boil, crack an egg into the fine-mesh sieve over a small bowl. Whirl the egg in the fine-mesh sieve, allowing the liquid egg white to fall through into the small bowl. Discard the liquid white. Carefully pour the egg in the sieve into its own ramekin. (The sieve should contain a yolk encased by a tighter egg white.) Repeat this process for the other eggs.
Once the water is simmering, create a vortex using a spoon. Holding 2 of the ramekins close to the water's surface, gently pour the eggs into the middle of the vortex and cook them for about 3 minutes.
While the eggs are cooking, heat the slices of Canadian bacon in a large skillet over medium-high heat for about 1 minute. Toast the English muffins.
After 3 minutes, using a slotted spoon, carefully remove the poached eggs. Gently dab the eggs with a paper towel to remove excess water. Repeat for the remaining eggs.
Assemble the eggs Benedict. Top each toasted muffin half with butter, a slice of Canadian bacon, and a poached egg. Spoon hollandaise sauce over the poached eggs. Serve immediately.