In a large resealable plastic bag, mix together olive oil, vinegar, garlic, oregano, thyme and steak seasoning. Add eye round and close bag. Shake to completely coat meat. Place on a plate and refrigerate for at least 4 hours.

Heat gas grill to medium-high. Lightly coat grill rack with oil.

Remove roast from bag, reserving marinade. Brown eye round on grill on all sides, about 10 minutes. Transfer eye round to a 15-3/4 x 11-1/4 x 3-inch disposable roasting pan. Place potatoes and carrots around meat and toss with marinade reserved from meat.

Reduce heat to medium-low. Place pan on grill, and cook, covered, for 30 minutes. Stir twice. Stir in Brussels sprouts and salt. Continue to grill, covered, for 15 minutes. Check internal temperature of meat. Take meat out of pan when internal temperature reaches 135 degrees on an instant-read thermometer (meat will continue to cook and should reach 145 degrees). Keep warm. Stir vegetables and continue to cook for 15 more minutes or until all vegetables are tender.