Preheat the oven to 350ºF. Line a baking sheet with parchment paper.

In a small pot, bring 1 1/3 cups vegetable broth to a boil. Add the buckwheat, cover, reduce heat to low, and simmer for about 15 minutes, until all the liquid is absorbed. If the buckwheat absorbs all of the liquid before it is tender, add a bit more broth, cover, and continue cooking. When done, remove the cover, fluff with a fork, and allow to cool.

In the bowl of a food processor fitted with the steel blade, process the nuts, oats, and flax to form a coarse meal. Add the beets, bell pepper, parsley, fennel, mustard, and salt, and process until almost smooth yet still slightly grainy.

Using a large ice cream scoop or 1/3-cup measuring cup, scoop the mixture onto the baking sheet and flatten into patties about ½-inch thick. Bake for 25 minutes, then gently flip the burgers and bake for another 15-25 minutes, until they are crisp on the edges. To grill the burgers, prepare as directed, then allow to cool completely (preferably overnight in the refrigerator). Grill just to heat through and serve.