1. Pulse first 3 ingredients in food processor until finely chopped.
2. Heat 1 tablespoon oil over medium-high heat in a skillet; turn down to medium, and cook onion, stirring occasionally, about 15 minutes or until golden brown. Add mushroom mixture, and cook, stirring, about 2-3 minutes or until liquid evaporates. Remove from heat, and let cool.
3. Stir cooled mushroom mixture into lentils, and combine with next 3 ingredients (through salt) until well-combined. Form mixture into 6 patties (about 1/2 cup each). Put cornmeal on a shallow plate, and coat burgers evenly.
4. Heat remaining 1 tablespoon oil in a nonstick skillet over medium heat, and cook burgers about 3 minutes or until golden brown on underside. Flip burgers, and top with cheese. Cook about 3 minutes more or until golden brown and cheese is melted. Serve burgers on buns topped with tomato and basil, if desired.