Preheat the oven to 425°F (220°C). A high roast temperature creates quick caramelization on the squash and potatoes so they develop a golden, slightly crisp exterior without drying out the interior.

Toss the diced butternut squash (240 g) and diced fingerling potatoes (200 g) in a large bowl with 1 tablespoon of extra-virgin olive oil, 2 teaspoons maple syrup, 0.5 teaspoon smoked paprika, 1/4 teaspoon of the sea salt, and 1/8 teaspoon freshly ground black pepper. Mix thoroughly so each piece is lightly coated — the oil conducts heat and the maple syrup encourages caramelization and a gloss on the vegetables.

Arrange the squash and potatoes in a single layer on a rimmed baking sheet lined with parchment or a well-seasoned sheet pan. Crowding causes steaming instead of roasting; a single layer ensures the surfaces brown evenly. Roast for 20–25 minutes, turning once halfway through, until pieces are fork-tender and have golden-brown edges.

While the vegetables roast, chop 80 g lacinato kale, remove stems, mince 1 clove garlic and finely chop 2 teaspoons fresh sage. Toast 30 g walnuts in a dry skillet over medium heat, shaking the pan for 2–3 minutes until fragrant and lightly browned — toasting intensifies nuttiness and adds crunch. Set walnuts aside.

When the squash and potatoes have 4–5 minutes left, heat a large skillet (preferably cast-iron) over medium heat and add the remaining 1 tablespoon olive oil. Add the minced garlic and chopped sage and cook for 30–45 seconds until aromatic — this blooms the herb and softens raw garlic flavor. Don’t brown the garlic aggressively or it will taste bitter.

Add the roasted squash and potatoes to the skillet with the garlic and sage. Toss to combine and spread in an even layer. Increase heat to medium-high and press gently with a spatula so the vegetables make good contact with the pan; leave undisturbed for 2–3 minutes to encourage crisping and fond development — the browned bits (fond) add deep, savory flavor.

Season the skillet mixture with the remaining 1/4 teaspoon sea salt and 1/8 teaspoon pepper, then fold in the chopped kale (80 g). The residual heat will quickly wilt the kale without overcooking; wilting it in the pan retains texture and color while marrying it with the roasted vegetables.

Taste and adjust seasoning — a small splash (1/2 tsp) of maple syrup can be added now if you prefer a brighter sweet note. If the pan seems dry, add the optional 1 teaspoon butter and swirl to finish; the butter adds silkiness and helps the flavors meld.

While the hash rests for a minute, heat a separate nonstick skillet over medium heat with 1 teaspoon neutral oil for frying eggs. Heat until the oil shimmers; a properly heated pan produces crisp, golden edges without sticking.

Crack 4 large eggs into the skillet and cook sunny-side up: cover the pan with a lid for 1.5–2 minutes so the whites set while the yolks remain runny. For extra-crisp edges, tilt the pan and spoon the hot oil around the whites as they cook (basting). Cooking the eggs covered gently steams the tops so you don’t overcook the yolks.

Divide the hash between two warm plates. Top each portion with two fried eggs. Scatter the toasted walnuts (30 g) and chopped chives or parsley (2 tsp) over the dish for crunch and freshness. Finish with a light grind of black pepper and an optional pinch of flaky sea salt.

Serve immediately so you get the contrast of crispy edges and runny yolks. Encourage diners to break the yolk and mix it into the hash — the yolk adds a rich, silky coating that ties the sweet and savory elements together.