Heat the oven to 425°F.
Cut the greens from the beets, scrub the beets clean, and wrap them in foil. Place the foil-wrapped beets in the oven and roast for 45-55 minutes, until tender. Cool enough to handle, then rub the skins off. Cool completely then slice into thick rounds (1/4″ – 1/2″ or so).
While the beets are roasting, scrub the sweet potatoes clean and slice them into thick rounds (1/4″ – 1/2″ or so). Toss the rounds with olive oil, salt, and smoked paprika. Lay them in a single layer on a parchment-lined baking sheet. Roast alongside the beets for 10 minutes, flip, then roast for another 10-15 minutes until soft and starting to show a few toasted spots. Cool completely.
Scatter the walnuts on another baking sheet. When the sweet potatoes are done, toast the walnuts for about 15 minutes, until fragrant and showing toasted spots. Shake the pan a few times during baking to make sure the walnuts toast evenly. Roughly chop the walnuts while they’re still warm from the oven. Allow to cool.
Last but not least, prepare the greens. Slice the onion into thin strips. Slice the beet leaves down the middle rib, and then crosswise into thin strips.
Warm a teaspoon of olive oil in a skillet over medium-high heat. Sauté the onions with a pinch of salt until they are very soft and beginning to brown, 10-15 minutes. Add the beet greens with another pinch of salt and stir until the greens are fully wilted. Sprinkle the vinegar over the top, scrape up any browned bits from the pan, and give the greens a taste. Add salt or pepper as desired.
Package all these ingredients in separate containers and refrigerate.
To Assemble and Serve the Stacks
Heat the oven to 350°.
Assemble the stacks one at a time inside an 9×13 or similar sized baking dish. Start with a beet round. Spread a good dollop of goat cheese on top of the beet. Top with a sweet potato round and a little pile of greens. Repeat once, ending up with two of each layer in your stack.
Wrap the stack in aluminum foil as pictured in the photos. It works best to pinch the ends of the foil together and fold the flaps back on themselves. Pinch the top of the foil tubes closed to shield the top layer of greens. Prepare and wrap the other stacks like this.