Prep the produce and mise en place: remove thick kale stems and stack the leaves, then slice very thin (this shortens cooking time and keeps the kale tender). Mince the garlic and squeeze the lemon. Having everything measured makes the quick finish smooth.

Toast the sourdough: heat a heavy skillet or griddle over medium-high heat. Add 1/2 tbsp olive oil and 1/2 tbsp butter (optional) and when shimmering, add the sourdough slices. Toast 1–2 minutes per side until deeply golden and crisp. Toasting on the skillet crisps the crumb and develops nutty, caramelized flavor that resists sogginess from the greens and yolk.

Cook the kale: reduce heat to medium, add the remaining 1 1/2 tbsp olive oil to the same skillet and swirl. Add the minced garlic and cook 20–30 seconds until fragrant but not brown (browned garlic tastes bitter). Add the sliced kale, a pinch of sea salt, and 1/4 tsp of the smoked paprika (reserve the rest for seasoning the eggs). Sauté 2–3 minutes, stirring, until the kale is wilted, glossy, and tender—this quick sauté preserves bright color and avoids stringy, overcooked greens. Finish with the lemon juice to lift flavors and a crack of black pepper.

Make a smoked-paprika oil: in a small bowl combine the remaining 1/4 tsp smoked paprika with 1 tsp olive oil (or melted butter) and a pinch of salt. Let sit for a minute to bloom the paprika—the oil captures and carries the smoke and color so it shows on the finished dish.

Fry the eggs: wipe the skillet clean and return it to medium heat, or use a second nonstick pan. Add 1/2 tbsp olive oil and let it heat until shimmering (not smoking). Crack two eggs into the pan, season with salt and pepper, and spoon hot oil over the whites near the yolks for an even set without overcooking the yolks. Cook until whites are set but yolks are still soft, about 2–3 minutes for sunny-side or up to 4 minutes if you prefer slightly firmer yolks. The hot oil and controlled heat create tender whites with lacy, flavorful edges while keeping yolks runny.

Assemble the toasts: place one toasted sourdough slice on each plate, mound half the sautéed kale on each slice (press lightly so it adheres), then gently lay two fried eggs on top. Spoon the smoked-paprika oil over the eggs and kale for a glossy, aromatic finish. Finish with a few flakes of sea salt and a crack of black pepper. The layering keeps the toast crisp and ensures each bite has bread, greens, and egg.

Serve immediately: serve while the eggs are warm and yolks still runny so diners can break into the yolk and mix with the kale and bread—this creates a rich sauce that soaks into the sourdough.