I didn't include the greens when I prepared this - I was only cooking for myself and it was really the egg I wanted. But oh my gosh .. this was some tasty French toast :) Recipe is from Gourmet magazine.
Butter a 1-quart shallow baking dish or a 9-inch pie plate. Arrange bread in 1 layer in dish.
Whisk together milk, 1 egg, and 1/4 teaspoon each of salt and pepper. Pour over bread. Sprinkle with cheese and press lightly to help bread absorb custard. Let stand until absorbed, 15 to 30 minutes.
Dot with butter and bake, uncovered, until puffed and golden, 20 to 25 minutes.
Bring 2 inches water to a boil with a few drops of vinegar in a small deep skillet or saucepan. Break each remaining egg into a cup and slide into water, spacing eggs apart. Poach at a bare simmer to desired doneness (we prefer firm whites with runny yolks, 2 to 3 minutes).
Meanwhile, toss greens with remaining 2 teaspoons vinegar, oil, and 1/8 teaspoon salt.
Divide pain perdu between 2 plates and top with salad. Lift eggs out of poaching liquid 1 at a time with a slotted spoon and place on top of salad. Lightly season eggs with salt and pepper.