For the tournedos: Heat 1 tablespoon olive oil in a medium pan over medium-high heat. Sprinkle the beef medallions on both sides with salt and black pepper. When the pan is hot, add the medallions and sear on both sides, cooking until the desired temperature is reached. Remove from the pan and let rest.
Reduce the heat under the pan to medium. Add the mushrooms, cut side down, and the green peppercorns and shallots. Cook, stirring occasionally, until mushrooms begin to brown and the shallots become translucent, about 5 minutes. Remove the pan from the heat and add the cognac. Replace the pan to the burner, and carefully tip to flambé. (If you don't wish to flambé, just bring the sauce to a boil and reduce to a simmer.) Once the flame has burned out, add the demi-glace, mustard and lemon juice. Cook, stirring, for a few minutes. Stir in the cream and reduce until the sauce is thick and rich in color, 3 to 5 minutes.
Add the beef medallions to the sauce, spooning sauce over so they are submerged. Remove the pan from the heat; stir in the butter and add some parsley. Keep warm.
For the matchstick frites: Heat 3 inches of vegetable oil in a Dutch oven to 365 degrees F.
Add the rosemary, sage, thyme and garlic and fry until the herbs are crispy. Remove to a paper towel-lined plate to drain.
Using a mandoline, cut the potatoes into matchsticks and place in a large bowl of ice water to remove any starch. Let soak for a few minutes, then rinse under cold water until the water runs clear. Drain the matchsticks and pat dry with a kitchen towel to remove as much water as possible.
Fry the matchsticks in small batches until crispy and golden, 2 to 3 minutes. Drain on a paper towel-lined baking sheet and sprinkle immediately with salt to taste.
Transfer the frites to a large bowl and toss with the crispy herbs and more salt to taste.
Serve the tournedos with the frites.
Use extreme caution when igniting alcohol. Remove the pan from the heat source before adding the alcohol. Pour the alcohol into the pan and carefully ignite with a match or click lighter. Return the pan to the heat and gently swirl to reduce the flames.