Prep and preheat: place a 10-inch ovenproof skillet (cast-iron is ideal) on the middle rack and preheat the oven to 425°F (220°C). Preheating the skillet ensures an immediate sizzle and lift when the egg mixture hits the pan — that shock of heat helps the edges set and the center rise.

Make the Parmesan crisp: scatter 2 tablespoons (roughly 15–18 g) of the grated Parmesan into a small nonstick skillet over medium heat in a thin round (about 3–4 inches wide). Cook without stirring for 90–120 seconds until the edges darken to golden and the cheese melts into a lacy disc. Transfer to a paper towel to cool and crisp. Doing this first avoids crowding the oven later and gives you a crunchy contrast to the soft eggs.

Caramelize the onion: add 1 tsp oil (or a small knob of butter) to a medium skillet over medium-low heat. Add the thinly sliced onion and a pinch of salt, and cook slowly, stirring every couple of minutes, for 8–10 minutes until soft and deep golden. Low-and-slow heat extracts the onion's natural sugars without burning, producing a sweet, savory base that pairs beautifully with eggs and cheese.

Separate eggs: carefully separate the 6 eggs into yolks (place yolks in a medium bowl) and whites (place whites in a large clean mixing bowl). Separating allows you to whip the whites for lift while keeping yolks rich and tender.

Whip the whites: add 1/8 tsp of the salt to the egg whites and whip with a hand mixer or whisk to soft peaks (when you lift the whisk, a soft peak that gently folds over). Whipping incorporates air — these bubbles are the reason the finished baked eggs will be cloud-like and airy.

Beat the yolks: whisk the egg yolks with 1 tbsp cold water, the remaining pinch of salt, and half of the grated cheddar (reserve the rest for finishing). A little water will create steam in the oven and help temper the yolk texture; folding in some cheese now ensures even cheesy pockets throughout.

Fold whites into yolks: gently fold one-third of the whipped whites into the yolk mixture to loosen it (this lightens the yolk base). Then fold in the remaining whites in two additions with long, gentle strokes — fold from the bottom to the top to preserve as much air as possible. Overmixing will deflate the air you've worked into the whites.

Butter the hot skillet: carefully remove the preheated skillet from the oven with oven mitts (it will be very hot). Add the 1 tbsp butter and swirl to melt and coat the pan — the sizzling butter gives the eggs a golden exterior and helps promote immediate oven-spring.

Bake the eggs: pour the egg mixture into the hot buttered skillet, smoothing the top lightly. Scatter the remaining cheddar evenly over the surface and spoon the caramelized onion in three small clusters (this lets pockets of sweet onion concentrate rather than weigh down the whole souffle). Immediately transfer to the oven and bake for 9–12 minutes, until the top is golden and the center is just set (it should wobble slightly). Baking at high heat sets the outside quickly while the interior remains tender and custardy.

Finish and rest: remove from the oven and let rest for 1–2 minutes; the eggs will settle slightly and finish cooking from residual heat. Break the Parmesan crisp into elegant shards and tuck them atop or alongside the baked eggs for contrast. Season with freshly ground black pepper and, if desired, a pinch more salt.

Serve: slide the baked eggs onto warmed plates or serve directly from the skillet family-style. The contrast of airy interior, melted cheddar ribbons, sweet onion, and crunchy Parmesan makes each bite multilayered and exciting.