1. Preheat the oven at 400 degrees F.
To make Cote Du Boeuf :
2. In a pan heat oil and sauté ribeye steak until browned on both sides.
3. In the same pan melt butter and sizzle thyme sprigs and garlic.
4. Roast in the oven at 400 degrees until internal temp is 125 degrees.
5. Remove from oven and let the meat rest for 10 minutes.
6. Sautee mushrooms in oil until browned
To make the Bernaise:
7. In a small saucepot, simmer together shallots, peppercorns, tarragon stems and white wine until reduced to sec, strain and cool.
8. In a mixing bowl, combine egg yolks and white wine.
9. Cook over a low flame to the ribbon stage, remove from heat and emulsify in melted butter.
10. Finish with chiffonaded tarragon and parsley.
11. Slice the steak.
12. On a serving plate spread the barnaise sauce, lay the beef slices and spoon over demi-glace.