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Season the steaks generously with salt and pepper. In a large skillet over medium-high heat, heat the oil until it shimmers, then add the steaks and cook, turning once, until evenly browned, 4–5 minutes for medium rare. Transfer to a plate to rest.
Meanwhile, return the skillet to medium-high heat and add the stock. Cook, stirring to deglaze, until the liquid is reduced by two-thirds, about 10 minutes. Pour the demi-glace into a heatproof bowl and set aside.
Return the skillet to medium-high heat and add the butter. When the butter is melted and the foam begins to subside, add the garlic and shallot, and cook, stirring frequently, until soft, about 2 minutes. Add the mushrooms and cook, stirring frequently, until they soften, release their liquid, and begin to brown, about 2 minutes more. Add the cognac, then carefully light with a long match or lighter to flambé, shaking gently until the flame dies down. Stir in the reserved demi-glace along with the cream, Dijon, Worcestershire, and Tabasco.
Return the reserved steaks to the skillet, lower the heat to simmer, and cook, turning to coat, until the sauce is thickened and the meat is warmed through, about 4 minutes. To serve, transfer the steaks to warmed serving plates; stir the chives and parsley into the sauce, and drizzle it over the steaks.