Grate the squash, parsnips, and onions using the shredding attachment on a food processor. Transfer to a bowl. Add the eggs, arrowroot, cinnamon, salt, and pepper. Mix well.
Add about ½ inch oil to a wide, deep skillet or Dutch oven and warm over medium-high heat. When the oil is hot, gently drop the squash mixture by scant ¼-cupfuls into the oil. Let cook for about 10-20 seconds, then gently flatten just a bit with a spatula. Cook for about 3 minutes, or until browned.
Carefully flip the latkes and continue cooking until the opposite side is browned. Transfer to paper towels to drain. Repeat with remaining butternut mixture. Serve immediately, or transfer to a baking sheet and keep in a warm oven until ready to serve.
To make the cashew crème:
Combine all ingredients in a food processor or high-speed blender. Adjust sweetener and seasonings to taste. Chill several hours before serving.