Remove the eye of round roast from the refrigerator about 30 minutes prior to preparing it and allow it to come to room temperature.
Preheat oven to 250°F and pat the roast dry with a paper towel. Cut the yellow onion into a large dice.
Combine the garlic powder, pepper, salt, rosemary and thyme in a small bowl. Rub the roast on all sides with the dry rub.
Heat oil in a large cast iron skillet over medium heat. When the oil is hot add the seasoned roast to the pan and sear on all sides - about 2 minutes each side. Turn off heat and remove the seared roast from the pan.
Add the onion to the bottom of the skillet in an even layer to create a natural roasting rack. Place the seared roast on the onions and pour broth into the pan.
Place the roast in the oven to bake at 250°F until the internal temperature reaches 125°F - the cook time will depend on the exact size of the roast so start checking the temperature at regular intervals using an electronic thermometer starting at 1 hour of cooking. It will take on average about 2 hours for a 3 pound eye of round roast to reach an internal temperature of 125°F
Remove the roast from the oven and transfer to a cutting board to rest for 15 minutes. Slice into thin slices against the grain. Strain the juice from the cast iron skillet and serve with the thinly sliced beef.
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