Adjust oven rack to middle position and heat oven to 450º. Spray rimmed baking sheet with vegetable oil spray. Shred potatoes with food processor or box grater then transfer to large bowl. Cover with cold water and let sit for 5 minutes. Drain potatoes in a colander and rinse and dry bowl. Using clean dish towel, squeeze potatoes dry in four batches, transferring dried potatoes to dry, now-empty bowl.
Add scallions, ¼ cup vegetable oil, 1 tsp salt, and ½ tsp pepper to potatoes and toss to combine. Distribute potatoes in even layer on sheet, but do not pack down. Bake until top of potatoes is spotty brown, 32 to 35 minutes.
Remove sheet from oven. Using metal spatula, flip hash browns in sections, then sprinkle kimchi evenly over top. Using back of spoon, create six 3-inch-wide indentations in potatoes. Crack 1 egg into each and sprinkle with ¼ tsp salt and ¼ tsp pepper.
Bake, rotating sheet halfway through, until whites are just beginning to set but still have some movement when sheet is shaken, 7 to 8 minutes for slightly runny yolks or 9 to 10 minutes for soft-cooked yolks. Season with salt and pepper to taste and sprinkle with cilantro. Serve.