Wash beets, pat dry. Place beets on a large piece of aluminum foil, folding edges up to create a pouch around the them. Roast at 375 for about 1 hour, or until beets are quite tender.
Allow to cool slightly, then rub the skins off the beets with some paper towels (or your bare hands – expect some staining!).
In a food processor, blitz roasted beets until smooth.
Measure 2 cups of puree into a large bowl, reserving the rest for a future use (can be frozen.) Allow to cool to room temperature before proceeding.
In a separate bowl, whisk together flours, starch, salt, and xanthan gum to combine well. Add flour mixture to cooled beet puree, gently fold to combine.
Add eggs, once again gently folding to combine. Cover tightly with plastic film, Chill for 1 hour.
Generously dust your work surface with potato starch. Dump gnocchi dough out, knead gently to bring together into a soft ball. If the dough is sticky, add a little potato starch until it’s workable.
Divide dough into 8-10 roughly equal pieces. One at a time, roll each out into long “snakes”, each about the thickness of a thumb. Cut each roll into bite-sized pieces, about ¾″- 1″ long.
If you’re feeling lazy, you can cook these up as-is. Otherwise, you can roll them over a fork to produce the traditional ridged gnocchi shape. There are many possible ways to do this, and you may want to play with it a bit until you find your own groove. For me, I gently (but firmly!) roll each gnocchi over the back of the fork, aiming towards the pointed ends of the tines. As I roll, the gnocchi will curl over itself into a slight “c” shape. Practice, experiment, and if necessary – Youtube has great tutorials for a variety of methods.
Start a pot of boiling water, and salt it well. Bring it to a gentle, not rolling boil, and cook your gnocchi in batches. As they float to the top, allow them to cook another minute or so before using a slotted spoon to remove them, transferring to a clean bowl or plate.
In a large nonstick pan, melt butter. Chop basil leaves, add to pan along with lemon juice, stir well. Cook for a few minutes, until butter starts to brown.
Add cooked gnocchi to the pan, toss to coat. Season with salt and pepper, to taste.
Serve hot, sprinkled with crumbled goat cheese