Preheat the smoker to 225°F.
In a small bowl, mix together the coarse salt, black pepper, smoked paprika, and minced garlic. Stir in the avocado oil to form a paste.
Rub the entire surface of the eye of round roast with the seasoning paste, ensuring it's evenly coated.
Place the seasoned roast directly on the smoker grates. Insert a meat thermometer probe into the thickest part of the roast to monitor its internal temperature throughout the cooking process.
Smoke the roast at 225°F for about 2.5 - 3 hours, or until the internal temperature reaches your desired level of doneness. For medium-rare, aim for an internal temperature of 130°F to 135°F. For medium, target 140°F to 145°F.
Once the roast reaches the desired internal temperature, carefully remove it from the smoker. Let it rest on a cutting board, tented with aluminum foil, for at least 20 minutes before slicing.
Slice the roast against the grain into thin slices.