Split the whole wheat English muffin and toast both halves until golden brown.
In a small skillet over medium heat, lightly sear the Canadian bacon slices for 1-2 minutes per side until heated through and slightly browned.
Prepare the clean hollandaise by whisking the Greek yogurt, one egg yolk, lemon juice, and Dijon mustard in a small heat-proof glass bowl.
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 3-5 minutes until the sauce is thickened and velvety.
Remove the sauce from heat and season with sea salt and black pepper.
Fill a separate medium saucepan with water, add the white vinegar, and bring to a very gentle simmer.
Carefully crack the two remaining eggs into the simmering water and poach for 3 minutes until the whites are opaque and set but the yolks remain runny.
To assemble, place two slices of Canadian bacon on each toasted muffin half, top each with a poached egg, and generously spoon the warm yogurt hollandaise over the top.
Garnish with freshly chopped chives and serve immediately.