How to Make It
Preheat the oven to 325°. Spread half the kale on a large rimmed baking sheet and bake for about 20 minutes, until dried. Let cool, then transfer to a food processor and grind into a powder. Sift the kale powder into a medium bowl.
Meanwhile, set up an ice bath in a medium bowl. In a medium saucepan of salted boiling water, blanch the arugula until tender, 2 to 3 minutes. Using a slotted spoon, transfer to the ice bath to cool. Drain well, then squeeze out the excess water and transfer to a blender. Add 3/4 cup of the grapeseed oil and puree until very smooth, about 2 minutes. Strain the arugula oil through a cheesecloth-lined fine sieve into a small bowl, pressing on the solids.
In a food processor, puree the goat cheese until just smooth. Add 1/4 cup of the arugula oil and puree until light and very smooth. Scrape the goat cheese into a medium bowl and season with kosher salt.
Set up another ice bath. Bring a medium saucepan of water to a boil. Using a slotted spoon, carefully lower the eggs into the water and simmer for 5 minutes and 30 seconds. Using a slotted spoon, transfer the eggs to the ice bath to cool completely. Carefully peel the eggs. Keep the water in the saucepan hot.
Light a grill or preheat a grill pan. In a medium bowl, toss the remaining kale with the remaining 1 tablespoon of grapeseed oil and season with kosher salt. Grill over high heat, turning occasionally, until lightly charred, 3 to 5 minutes. Transfer to a plate and use a spray bottle to spritz lightly with apple cider vinegar, if desired.
Decoratively spoon the whipped goat cheese into the center of 4 plates and arrange the grilled kale around it. Using a slotted spoon, carefully lower the peeled eggs into the saucepan of hot water and warm for 1 minute, then transfer them to a paper towel–lined plate to drain slightly. Coat the eggs in the kale powder and place them on the goat cheese mounds. Sprinkle with flaky sea salt and dust with more kale powder. Serve right away.