1. Preheat oven to 350 degrees. Melt 2 tablespoons butter, toss with brioche cubes, and spread on a rimmed baking sheet. Toast until golden and crisp, about 8 minutes. Let cool completely.

2. Melt remaining 5 tablespoons butter in a large saucepan over medium heat. Add flour and cook, stirring, until golden, 2 to 3 minutes. Whisk in 3 cups milk and 1 1/2 teaspoons salt. Cook, stirring, until mixture is thick enough to coat the back of a wooden spoon, about 10 minutes. Remove from heat; stir in nutmeg and pepper to taste. Press parchment paper directly on surface of bechamel to cover.

3. Place half of spinach in a large pot over medium-high heat. Cover and cook just until spinach wilts, about 2 minutes. Add remaining spinach, cover, and cook until it collapses, about 2 minutes more; drain. When cool enough to handle, squeeze as much liquid from spinach as possible. Coarsely chop and stir into bechamel.

4. Bring 1 1/2 inches of water to a simmer in a large, deep skillet over medium-high heat. Stir in vinegar. Crack 1 egg into a small bowl. Holding bowl just above surface of water, gently pour egg into skillet. Repeat with 3 more eggs. Poach eggs, adjusting heat to maintain a simmer, just until whites are firm and yolks are still runny, about 4 minutes (for firmer yolks, poach 1 to 2 minutes more). Gently remove eggs from water with a slotted spoon, allowing excess water to drain, and transfer to a plate. Poach remaining eggs in 2 more batches. Use immediately or transfer to a bowl of ice-cold water.

5. Uncover creamed spinach and heat with remaining 1/4 cup milk in a saucepan over medium heat, stirring, until warmed through. If necessary, transfer poached eggs to a large pot of simmering water with a slotted spoon and cook until warmed through, about 30 seconds. Divide spinach evenly among 12 small ramekins or bowls, top with poached eggs and croutons, and season with salt and pepper. Serve immediately.