Meanwhile, in a super hot large sauté pan, add half canola oil and look for smoke.
When smoking, add 1 pound of the mushrooms, (making sure they are cleaned with stems broken off the bottoms-don’t ever use water to clean mushrooms-if dirty, just wipe with a kitchen towel).
Sauté mushrooms until golden brown, and at the end, add half the butter, 2 sprigs of thyme, and one shallot shaved.
Toss mushrooms to get easily coated with the butter mix, and when slightly crunchy and browned, pour out onto cooling rack, letting the butter fall to the bottom to strain the mushrooms.
Repeat this step with the second pound until all mushrooms are cooked.
While hot, toss the mushrooms into a mixing bowl with the frisee, anchovy vinaigrette, and parsley leaves.
Mix well and serve warm.