To prepare the Tomato-Basil Relish: In a small bowl, stir together tomatoes, cucumber, green onion, vinegar, 1 Tablespoon basil, and ⅛ teaspoon pepper. Cover and chill for at least 4 hours or up to 24 hours.
To prepare the Feta-Stuffed Burgers: In a bowl, stir together egg product and water. Stir in oats, ¼ teaspoon pepper, and salt. Add beef; mix well. Shape mixture into twelve ¼-inch-thick patties. Spread mustard on one side of 6 patties. Top with crumbled cheese. Place remaining patties on top of cheese, pressing edges to seal.
For charcoal grill, place patties on the rack of an uncovered grill directly over medium coals. Grill for 12 to 14 minutes or until meat is done (160°F). (For a gas grill, preheat grill. Reduce heat to medium. Place patties on grill rack over heat. Cover and grill as above.)
Serve patties on toasted English muffin halves. Top with Tomato-Basil Relish. If desired, garnish with fresh basil. Makes 6 burgers.