Mushrooms: Make the BBQ pulled mushrooms using this recipe (5 minutes hands-on work, 25 minutes cooking).
Hollandaise: In a large heat-proof bowl, whisk together yolks and lemon juice. Set over a pot of simmering water (so that the bottom does not touch the water, but is heated by the steam) and continue whisking. When mixture has thickened and is foamy (3 min), slowly pour in the butter, whisking quickly to ensure it is completely emulsified. Continue whisking until mixture is thick. Add a dash of salt, give it one more stir, then remove from heat, cover, and set aside.
Eggs: Bring a pot of water to a boil, then reduce to a gentle simmer. Pour white vinegar into the pot. Crack an egg into a shallow bowl, then slowly lower the egg into the simmering water. Cook 3 to 4 minutes, or until yolk is a little less jiggly. You may need to work in batches here. Place poached eggs on a paper towel to remove excess moisture.
Assemble: Slice English muffin or bun in half and toast. Top with BBQ pulled mushrooms, poached egg, and Hollandaise sauce. Garnish with a pinch of cayenne pepper and chives.