In a small saucepan cook green onion and garlic in the broth, covered, about 2 minutes or until onion is tender. Add soy sauce, lemon peel, lemon juice, chili powder, and brown sugar. Bring to boiling; reduce heat.
Simmer sauce, uncovered, for 5 minutes, stirring the mixture frequently. Stir in the peanut butter and the gingerroot or ginger; let mixture heat gently through, without boiling.
Thin sauce with a little unsweetened coconut milk, if desired. Serve at room temperature. Cover and refrigerate the peanut sauce to store. Makes about 1-1/2 cups.