Prep and measure: Thinly slice the white and light-green parts of the leek, separate 4 eggs for the batter and 4 eggs for poaching, shred the Gruyère, and measure milk and flour. Mise en place shortens cooking time and ensures nothing is forgotten when the batter and oven are hot.

Caramelize the leeks: Melt 28 g (2 tbsp) of the butter in a wide skillet over medium-low heat. Add the sliced leeks and a pinch of salt, and cook gently for 12–18 minutes, stirring occasionally. Lower heat and slow cook to draw out moisture and allow natural sugars to brown — this is what turns sharp raw leek into sweet, savory, jammy flavor. If the skillet starts to stick, add 1 tsp olive oil or a splash of water; do not rush with high heat or they will burn.

Season the leeks and finish: When the leeks are deeply golden and soft, stir in a small pinch of black pepper and 1/2 tsp of white wine vinegar to brighten the sweetness. Transfer to a bowl and leave any fond in the pan — the fond will help flavor the Dutch baby when you melt the butter for baking.

Make the batter: In a medium bowl whisk together 4 large eggs and 1 tsp kosher salt until slightly frothy. Whisk in 120 g all-purpose flour until combined; pour in 240 ml whole milk slowly while whisking to make a smooth, lump-free batter. Add a pinch of nutmeg if using and 1/4 tsp freshly ground black pepper. The eggs provide structure and lift; whisking them first ensures an even batter and prevents flour lumps.

Rest the batter: Cover the batter and rest at room temperature for 30 minutes. Resting hydrates the flour and allows gluten to relax, which helps the Dutch baby develop an even, custardy interior and better oven lift.

Preheat the oven and skillet: Place a 12-inch (30 cm) cast-iron skillet or ovenproof skillet in the oven and preheat to 220°C (425°F) for at least 20 minutes. Heating the pan until it's very hot is essential — the batter hits the hot butter and skillet and immediately produces steam, which makes the edges rise dramatically.

Melt the butter in the hot skillet: Remove the preheated skillet from the oven using heavy mitts. Add the remaining 28 g (2 tbsp) butter (and 1 tsp olive oil if using) to the skillet; it should sizzle and foam. Swirl to coat the bottom and sides quickly — the sizzling butter creates steam against the batter and contributes nutty, brown-butter flavor. Work quickly to avoid burning the butter.

Combine and bake: Give the rested batter a quick whisk (it may separate slightly while resting). Pour the batter into the hot, buttered skillet, then scatter the caramelized leeks evenly across the batter, and top with most of the shredded Gruyère (reserve a small handful for finishing). Pop the skillet into the oven and bake for 16–18 minutes, until the edges are puffed high and deep golden brown and the center is set but still custardy. Do not open the oven during the first 12 minutes — changes in oven temperature will reduce lift.

Finish under the broiler if needed: If the top is not as golden as you like after the time is up, switch to broil for 1–2 minutes to color the cheese and edges. Watch closely — broilers work fast and you do not want the cheese to burn.

Poach the eggs (while the Dutch baby bakes): Bring a wide saucepan of water to a gentle simmer (small bubbles, not a rolling boil). Add 1 tbsp white wine vinegar and a pinch of salt. Crack 1 egg into a small cup and gently slip into the simmering water. Poach 3–4 eggs at a time in gentle water for 3–3½ minutes for a tender set white and runny yolk. The vinegar helps coagulate the whites quickly and keep them tidy. Use a slotted spoon to lift poached eggs and transfer to a bowl of warm water to hold briefly while the Dutch baby finishes.

Rest and plate: Remove the Dutch baby and allow it to sit for 1 minute — it will deflate slightly as steam escapes (this is normal). Scatter the remaining Gruyère so it melts on the hot surface, then top with the poached eggs (one per portion), a sprinkle of chopped chives, finishing salt, and freshly ground black pepper. The hot Dutch baby will melt the cheese and warm the eggs without overcooking them.

Serve immediately: Slice into four wedges and serve right away. Dutch babies puff spectacularly in the oven but begin to fall as they cool, so serving immediately preserves the contrast between crisp edges and the tender center.