- 1 large butternut squash–peeled, halved lengthwise and seeded
- 1/3 cup maple syrup
- 1½ tablespoons extra-virgin olive oil
- ¼ teaspoon smoked paprika (pimentón)
- ½ teaspoon kosher salt, divided
- ¼ teaspoon freshly ground black pepper, divided, plus more to finish
- ½ teaspoon distilled white vinegar
- 4 large eggs
- 3 cups baby arugula
- ½ small red chile, finely chopped (preferably a Fresno chile)
- 1½ teaspoons fresh lemon juice
- Flaky sea salt for serving
1. Adjust an oven rack to the lowest position and another rack to the middle position. Set a baking sheet on the lowest rack and preheat the oven to 400°. Set the squash on a cutting board and cut in half crosswise to separate the neck from the round bottom. Chop the bottom half into ¼-inch cubes and place in a medium bowl. Stand a long piece on its end and carefully slice lengthwise into 2 equal “steaks,” each about ¾ inch thick. Repeat with the other long piece of squash.
2. In a small bowl, whisk together the maple syrup, olive oil, smoked paprika, ¼ teaspoon of the salt and ⅛ teaspoon of the pepper. Drizzle 3 tablespoons of the maple-syrup mixture over the chopped squash cubes and transfer the mixture to a baking sheet (not the baking sheet in the oven).
3. Use a pastry brush to coat one side of the squash steaks with the remaining maple syrup mixture. Transfer the steaks, maple side down, to the preheated sheet pan and sprinkle the top side with the remaining ¼ teaspoon salt and ⅛ teaspoon pepper. Place the baking sheet with the steaks on the bottom rack of the oven and place the baking sheet with the diced squash on the middle rack. Roast until the squash steaks and cubes are tender and the steaks begin to caramelize, about 15 minutes. Remove both baking sheets from the oven and set aside to cool slightly.
4. In a medium saucepan set over medium heat, add the vinegar and enough water to reach 3 inches up the sides of the pan. Bring to a boil. Working one at a time, crack each egg into a small bowl and carefully tip the egg into the boiling water. Repeat with another egg. Use a slotted spoon to baste the eggs, cooking until the whites are set, about 2 minutes. Use the slotted spoon to carefully transfer the eggs, one at a time, to a paper-towel-lined plate, and repeat with the remaining eggs.
5. In a medium bowl, combine the arugula and red chile. Season with the lemon juice, add the diced squash and toss to combine. To serve, divide the squash steaks among 4 plates. Top with the arugula-squash mixture. Carefully place a poached egg over the arugula, sprinkle with sea salt and black pepper and serve immediately.