In medium saucepan, prepare bulgur according to package directions, omitting salt and substituting 1 1/3 cups broth for water. Fluff with fork.
In food processor or blender, process basil, walnuts, garlic, salt, cayenne and remaining broth until smooth. Stir basil mixture, bell pepper and green onions into bulgur.
In large skillet, bring water and vinegar to boil over high heat. Reduce heat and simmer. Break one egg into cup then carefully slip egg into simmering water. Repeat with remaining eggs, placing in water so they don't touch. Simmer 3-5 minutes, or until whites are completely set and yolks are beginning to set but aren't hard. Using slotted spoon, drain eggs well and place on bulgur mixture. Serve with lemon wedges.
Notes
Note: White vinegar helps firm egg whites quickly, preventing them from spreading too much.