Place the cashews in a small bowl and add enough water to cover the nuts. Set aside until ready to make the dip, about 5 minutes.
Combine the drained cashews, beets, beet juice, dill, lemon zest and juice and cucumber in the carafe of a food processor. Pulse into a smooth paste, about 2 minutes, scraping down the sides of the carafe as needed. While the machine is running, stream in the olive oil. Turn off the machine and season the dip with salt and pepper. Pulse until just combined and pour into a serving bowl. Garish with a drizzle of olive oil, chopped dill, and crumbled feta cheese. Serve with potato chips. Store in an airtight container in the refrigerator for 1 week.
Leave the skins on the potatoes and slice as thinly as you can manage; you can also use a mandoline if desired. Pat dry with a paper towel. Heat enough oil to fill a heavy-bottomed pot or Dutch oven halfway to 375 degrees F. Drop in the potatoes in batches and fry until crisp and starting to brown on the edges, 1 to 2 minutes. Remove to wire rack-lined baking sheet pan and sprinkle with some salt.