Pre-heat your oven to 450 °F (≈232 °C). Line a baking sheet with parchment paper (spray lightly with oil if desired) so the whites don’t stick.
Carefully separate the egg whites and yolks. Place the yolks individually into small bowls and set aside.
In a perfectly clean, dry mixing bowl (glass or stainless steel), whip the egg whites with an electric mixer on high speed until stiff peaks form — thick, glossy peaks that hold their shape when you tilt the bowl.
Gently fold in the sea salt, black pepper, grated cheddar and chopped chives/parsley into the whipped whites, using a spatula and taking care not to deflate the volume—this is where that airy texture comes from.
Spoon the whipped mixture into four mounds on your prepared baking sheet. Using the back of the spoon, press a gentle well or indentation into the centre of each mound (about the size of a yolk) so the yolk can sit snugly later.
Bake the whites alone for 3 minutes until the tops are just set and the edges begin to turn lightly golden. You’ll hear the very faint sizzle of the whites setting.
Carefully remove the sheet, and using a small spoon, gently nestle one egg yolk into each well without breaking the yolk. Return to the oven and bake for another 3–4 minutes, until the yolk is just set around the edges but still soft in the centre (or longer if you prefer firmer yolks).
Remove from oven and immediately season with a sprinkle of smoked paprika if using and a drizzle of olive oil. Serve right away while still warm and the whites are airy and crisp at the edges.