Place the prepared potatoes in a large pot and fill with water. Bring to a boil over medium-high heat and cook until the potatoes are fork tender, about 20-25 minutes.
While the potatoes are cooking heat a small saucepan over low heat with the coconut milk and Earth Balance. Keep warm.
When the potatoes are easily pierced with a fork drain them into a colander and pour them back into the pot.
Pour the warm coconut milk mixture over the potatoes and mash with a potato masher until smooth adding additional coconut milk 1 tablespoon at a time if needed.
Fold in the caramelized onions and chives until fully incorporated. Season liberally with salt and pepper.
Spread the mashed potatoes onto a sheet pan about 1/2-inch thick and place it into the refrigerator to chill for 6-8 hours or overnight. Your mashed potatoes should firm up and harden in the fridge.
Line a baking sheet with parchment paper, set aside. When the potato mixture has cooled enough to harden use a 1- 1 1/2-inch circle cutter to cut out as many circles as you can. (About 28-30) Then use a 1/2-inch circle cutter to cut holes from the center of the larger circle creating a donut shape. Mix the flours together in a shallow dish and season with salt and pepper. Place the cashew cream in a separate shallow container. Dip the rings in the cashew cream and then into the flour mixture. Place the battered rings onto the prepared baking sheet and freeze until solid, about 4-6 hours.
When the rings are frozen solid heat the vegetable oil to 375°F in a large shallow pot. Drop the frozen, battered rings into the oil a few at a time and fry for 4-6 minutes until golden brown. Serve immediately.