Whisk the Greek yogurt, one egg yolk, melted ghee, lemon juice, and Dijon mustard in a small heat-proof bowl until completely smooth.
Place the bowl over a small pot of simmering water to create a double boiler, whisking constantly for 3-5 minutes until the sauce thickens into a velvety consistency.
Remove the sauce from heat and season with sea salt and black pepper, then set aside in a warm spot.
Fill a medium saucepan with water, add the white vinegar, and bring to a very gentle simmer.
Crack the remaining two eggs into separate small ramekins, then carefully slide them into the simmering water to poach for 3 minutes until the whites are set but the yolks remain runny.
While the eggs poach, lightly sear the Canadian bacon in a skillet over medium heat for 1-2 minutes per side until warmed and slightly browned.
Split and toast the whole wheat English muffin until golden and crisp.
Place two slices of Canadian bacon on each toasted muffin half, top with a poached egg, and generously drizzle with the warm hollandaise sauce.
Garnish with freshly chopped chives and serve immediately.