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Step 1
Slather the roast with the olive oil on all sides, then season the roast with the salt, garlic, and black pepper. Place the roast into a large freezer bag; seal the bag and place it into a bowl in the fridge. greased 12-inch cast iron skillet or your favorite roasting pan.
Step 2
1-2 hours before you want to cook the eye of round roast, remove it from the plastic bag and let it rest on the counter, uncovered. This will let the roast rest and also removes the chill from the meat so it can cook much move evenly.
Step 3
Preheat the oven to 450 degrees F. Place the prepared roast into a greased 12-inch cast iron skillet or roasting pan, then into the oven on the center rack. Roast the meat, uncovered, for 20-25 minutes or until very nicely browned all over the top and bottom.
Step 4
Reduce the oven temperature to 325 degrees F.; continue to cook the roast, uncovered, for 45-60 minutes, just until it reaches 125 degrees F. at the center of the roast. Begin testing the internal temperature of the roast at about the 40 minute mark to be sure you don't overcook the roast - this is very important.
Step 5
When the roast reaches the internal temperature of 120-125 degrees F. at the center, remove it from the oven, placing it onto a large cutting board. Cover the roast well with foil; let the roast rest for 20-30 minutes.
Step 6
While the roast rests, make the pan sauce. Over medium heat, add the wine to the drippings in the skillet or roasting pan; use a whisk to remove any of the attached bits of fond that are stuck to the bottom of the skillet. Continue whisking until the wine is nearly evaporated, then stir in the broth and heat until simmering.
Step 7
In a small bowl, combine the butter with the flour to form a paste, then add to the simmering broth, cooking over medium low for 8-10 minutes or until nicely thickened; season the sauce to taste with salt and pepper.
Step 8
Using a sharp carving knife, cut the roast into slices, across the grain. Place the slices onto plates; drizzle with the pan sauce, as desired.