Let the rib-eye roast sit at room temperature for 2 hours.

Preheat oven to 250 degrees Fahrenheit.

Heat a large skillet over medium-high heat.

Rub the roast on all sides with olive oil, salt, and black pepper.

Add roast to hot skillet and brown on all sides, about 10 minutes.

Transfer roast to a plate.

When cool enough to handle, rub minced garlic and rosemary all over the roast.

Pour off all but 2 tablespoons of the beef drippings from the skillet.

Add sliced portabella mushrooms to the skillet and sauté until well browned, about 8 minutes.

Mix chicken broth, red wine, and Dijon mustard.

Add the broth mixture to the mushrooms and simmer to blend flavors and reduce slightly, about 3 minutes.

Pour the mushroom sauce into a bowl and set aside.

Set a wire rack over the skillet (or use a regular roasting pan with a V-rack).

Set the roast on the rack.

Slow roast in the preheated oven for 2 1/2 to 3 hours, until the meat reaches an internal temperature of 135 degrees Fahrenheit for medium-rare or 140 degrees Fahrenheit for medium.

Transfer roast to a cutting board and remove rack from skillet.

Pour off excess fat, if any, from the skillet.

Set skillet over medium-high heat.

Return the mushroom sauce to the pan and heat to a simmer.

Add cornstarch dissolved in water and simmer until sauce thickens slightly, about a minute.

Carve the meat and serve with the sauce.