Preheat the oven to 450 degrees.
Coat the mushrooms with the olive oil, season with salt, and place in a baking dish or ovenproof skillet. Transfer to the oven and roast for about 20-25 minutes. Flip and cook for 5-10 more minutes. Remove from the oven and set aside.
Meanwhile, place the butter in a small pot over low heat and slowly bring to a simmer. Cook over low heat until the butter separates. When the milk solids fall to the bottom and the golden butter-fat rises to the surface, remove from the heat. Set aside.
Crack the eggs into a medium-sized bowl and add the cream. Add the pepper and whisk until well incorporated and foamy. Preheat an ovenproof pan over medium heat. When the pan is heated, add 2-3 tablespoons of the clarified butter.
Reduce the heat slightly. Using a 4-ounce ladle, add 1 ladle of eggs into the pan. Using a spatula, start stirring quickly. (This is to heat the eggs through so they set like custard.) Keep swirling them around so the eggs aren't in one spot long enough to burn. Once the eggs begin to set, stop stirring. Transfer to the oven and cook for 1 ½ minutes. (When you remove the omelette from the oven it should still have a soft-custard touch.)
Season with the chopped herbs, a pinch of sea salt, and cracked white pepper. Using an oven glove to hold the handle, tip the pan sideways and roll the omelette onto a plate with a spatula. Add some mushrooms and a few watercress leaves to the top of the omelette and serve. Repeat for 5 more omelettes.
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