Whisk the egg yolk, Greek yogurt, lemon juice, and Dijon mustard in a small heat-proof bowl until completely smooth.
Place the bowl over a small pot of simmering water, ensuring the bottom of the bowl does not touch the water, and whisk constantly for 3 to 5 minutes until the sauce thickens.
Season the hollandaise sauce with sea salt and black pepper, then remove from the heat and cover to keep warm.
In a non-stick skillet over medium-high heat, sear the Canadian bacon for 2 minutes per side until lightly browned and fragrant.
Split the whole grain English muffin and toast both halves until golden and crisp.
Fill a medium saucepan with water and add the white vinegar; bring to a very gentle simmer.
Crack each egg into a small ramekin, create a gentle whirlpool in the simmering water with a spoon, and carefully slide the eggs in.
Poach the eggs for exactly 3 minutes for a runny yolk, then remove with a slotted spoon and drain on a paper towel.
Assemble by placing two slices of Canadian bacon on each toasted muffin half, followed by a poached egg.
Drizzle the warm Greek yogurt hollandaise over the eggs and garnish with freshly snipped chives before serving.