Preheat the broiler on high. Make 4 sandwiches, but cutting the baguette in half lengthwise, and into 4 crosswise. Spread cheese on both sides of the bread. On 1 side of each sandwich arrange the egg slices. On the other side, spread out the tomato slices. Put on a baking sheet and broil until the edges begin to turn golden, about 1 to 2 minutes. Drizzle each sandwich with a few drops of balsamic vinegar and sprinkle with green onions. Arrange on serving plates and serve.
Lay the eggs in a single layer in a large saucepan. Cover with cold water by at least 1-inch. Bring to a boil. Cover with a lid, turn off the heat, and allow the eggs to sit for 15 minutes. Rinse with cold water.