Make the hollandaise sauce by whisking the egg yolks, lemon juice, cayenne, and salt in a heatproof bowl.
Place the sauce on a double boiler over medium heat, constantly whisking and slowly adding the ghee until the sauce thickens.
Remove the bowl, set aside, and cover to keep warm.
Remove stems from mushroom caps. Remove gills, if desired.
In a large bowl, toss mushroom caps in olive oil, salt, and pepper.
Place mushrooms on a hot grill stem side down over medium-low heat. Allow to cook on each side for approximately 4 minutes. The caps should shrink in size and be slightly charred.
While caps are grilling, get ready to poach the eggs.
Bring a pot of water with 1 tbsp. of apple cider vinegar to a light simmer; break the eggs carefully in the pot, one at a time, and cook about 3 minutes.
Put egg on top of mushroom cap and pour hollandaise sauce on top.
For parsley asparagus: Remove tough ends of asparagus.
In a large bowl, toss asparagus in 2 tbsp olive oil, salt, and pepper.
Place asparagus on a hot grill, over medium-low heat. Cook for several minutes until tender and slightly charred. Be sure to turn asparagus frequently to avoid burning.
In a blender, mix together parsley leaves with remaining olive oil, almonds, salt, and pepper. Blend until the mixture takes on the look and texture of pesto.
Cover asparagus with parsley and serve.