1. Place links in nonstick skillet. Add 1/4-inch water. Cook, uncovered, over medium heat until water evaporates. Remove links from skillet. Diagonally slice.
2. Wipe skillet out with paper towel. In medium bowl beat together eggs, milk, 1/4 cup onions, thyme, salt and pepper.
3. In same skillet melt butter, tilting to coat pan. Add egg mixture. Cook over medium heat, stirring occasionally, until set. Sprinkle with links. Top with cheese. Let stand for 1 to 2 minutes or until cheese melts. Sprinkle with additional sliced green onions, if desired.
*Note: For a lower fat version, replace the 6 eggs with 1 1/2 cups refrigerated egg substitute.