Place your beef ribeye roast in a large roasting pan on a rack. Using a rack makes for even cooking. If you don't have one, use a regular baking dish or cast iron pan. Be sure your roast is at room temperature (let it sit out at room temperature for about 1-2 hours before cooking).
Combine the unsalted butter, salt, pepper, herbs and garlic in a small bowl until well combined.
Pat the beef roast dry on all sides with some kitchen paper towel and rub the butter mixture all over the roast, making sure to coat all sides.
Place the roast in the oven at 425 degrees and set the timer for 15 minutes.
After 15 minutes, turn the oven temperature down to 350 degrees Fahrenheit and roast for about 50 minutes to 1 hour and 20 minutes. Check the internal temperature after about 50 minutes. Remove the roast as soon as the internal temperature reaches 120 degrees Fahrenheit (48 Celsius) for medium rare.
Once you remove the roast from the oven, use the rack to remove the roast from the roasting pan and let it sit on a cutting board for about 15 minutes before slicing. Loosely tent some foil over the top to keep it warm.
For the Au Jus:
Place the roasting pan on the stovetop over medium heat and use a whisk to scrape any bits off the bottom of the pan. Feel free to skim the fat off the top of the beef drippings before placing it over the heat, but if you're making this recipe for a holiday dinner leaving the fat in the drippings will make the au jus nice and rich.
Add the wine and Worcestershire sauce to the drippings and whisk them together.
Add the flour to the beef stock and whisk to combine. Pour the stock mixture into the pan with the drippings and continue whisking the mixture, until it thickens just slightly.
Taste, and season with salt and pepper to your tastes.
Place a fine mesh strainer over a bowl and strain the au jus to remove any impurities.
If you wish, add a tablespoon of butter to the strained au jus and stir it in to the sauce as it melts.
Slice the beef ribeye roast into thick slices (a 6-pound roast should serve 6-8 people generously) and serve with the au jus gravy and your favourite side dishes.
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Notes
Removing the roast when it reaches 120 degrees Fahrenheit ensures that the roast will stay nice and juicy on the inside and not overcook. The roast will increase in temperature slightly as it rests.Cooking past medium rare is not recommended as it will result in a tough texture.Use a probe thermometer instead of an instant-read thermometer is a good way to avoid opening your oven repeatedly. Simply place the probe into the centre of the roast, set it to the desired temperature, and the thermometer will let you know when the roast reaches the desired temperature.