Preheat oven to at 450°F. Remove greens and stems from beets. Set aside.
Roast beets whole in tinfoil with a drizzle of olive oil and sprinkle of salt for 45 minutes. Let cool and then remove skins carefully.
Chop reserved beet stems into equal 6” pieces. Divide amongst 2 mason jars.
In a small sauce pot, heat apple cider vinegar, 1 1/2 cups water, white sugar, and 1 tbsp kosher salt over high heat until lightly boiling. Pour into mason jar to completely cover beet stems.
To make pasta doughs, place 2 cups of flour in each of two medium mixing bowls.
In a blender, puree 1 large roasted beet with 1/2 cup water. Pour the puree into one bowl of flour.
Add 2 egg whites to the blender, which should have barely and puree left. Blend just until combined, which should create a light pink color. Pour into second bowl of flour.
One at a time, mix each bowl of flour and liquid into a stiff pasta dough. Knead each for 10-15 minutes until smooth and elastic.
Cover each dough with plastic and let rest in fridge for at least 2 hours, ideally 3-4 hours or overnight.
To make filling, heat a large sauté pan over medium heat. Add 4 tbsp unsalted butter and cook until melted and lightly browned. Add 5 cups of beet greens (or Swiss chard leaves) and cook down in the butter until soft.
Deglaze the pan with 1/4 cup heavy cream and stir to combine. Let cool slightly, then work in the chèvre, parmesan, and ricotta.
Let cool completely, then transfer filling to a large piping bag. Let chill in the fridge for 1-2 hours until cool and firm.
To make beet beurre blanc, start by cooking down white wine in a small stock pot over medium-high heat with one chopped up roasted beet, for about 8-10 minutes (until reduced by 75%).
Remove from heat and add your butter, stirring to combine. Let cool completely, then blend on high speed until smooth and bright pink.
To caramelize walnuts, heat a medium sauce pot over medium-high heat with just your 1 cup of shelled walnuts. Toast them, stirring frequently, for 1-2 minutes until fragrant.
Add your brown sugar and turn the heat down to medium. Stir constantly with a nonstick spatula until the sugar melts and coats all nuts in a glossy brown syrup.
Remove pan from heat and pour onto a waxy paper plate or a silicon-mat-lined baking sheet. Sprinkle with a little salt and let cool completely.
With your remaining beet, slice into very thin discs and pat dry with paper towels. Heat neutral oil over medium-high heat in a medium stock pot until 375°F.
Fry beet chips for 2-3 minutes, turning with a spider to crisp each side evenly. Because of the sugars in the beets, be careful of burning.
Transfer beet chips to a paper towel-lined baking sheet and let cool.
To assemble beet ravioli, remove your pasta doughs from fridge and from plastic wrap. Coat each in a light amount of flour and cut into 4 equal pieces.
Roll each pasta piece through your pasta roller, starting with the “1 setting”, working gradually to the “5” thinness setting. You should have a long and thin rectangular sheet.
Place each sheet on top of the next, pressing to adhere, starting with your dark pink dough, then your light pink dough, until you have no dough left.
Roll your stack of pink doughs into a log, starting at the short end. Slice your log into very thin discs and roll gently with a rolling pin or on the “5 setting” of your pasta machine.
Pipe a dollop of cheese and greens filling onto one pasta circle, then press another circle on top to adhere. Crimp around the filling to ensure it doesn’t leak during boiling.
Heat about 8 cups of water over high heat in a large pot until rapidly boiling. Season with a little salt and add your ravioli, about 8-10 at at time.
Cook for 2-3 minutes until the ravioli float, then remove from water with a spider tool and shake off excess water. Place each batch of ravioli on each plate.
Top each plate of ravioli with a generous few spoonfuls of beet sauce. Then, garnish with candied walnuts, fried beet chips, basil leaves, pickled beet stems, and a light sprinkle of salt.