- 6 (1-inch-thick) slices baguette, cut on a diagonal
- 1 cup whole milk
- 3 large eggs, divided
- 1/2 cup grated parmesan
- 1 tablespoon unsalted butter, softened
- 2 teaspoons red-wine vinegar plus a few drops for cooking eggs
- 3 cups baby greens (2 ounces)
- 1 tablespoon extra-virgin olive oil
- Preheat oven to 400°F with rack in middle.
- 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.