In a saucepan, bring quinoa, vegetable stock and sea salt to a boil. Reduce to a simmer, cover, and cook until liquid is absorbed, about 20 minutes. Remove from heat and allow to cool.
Meanwhile, place next 11 ingredients (through egg white) in a food processor or blender and mix until combined.
Add the seasoning mix and the quinoa flour one spoonful at a time to the cooled quinoa. Mix to combine.
Roll and mold the mixture into 16 ¼-inch patties, and place them on a parchment-lined baking sheet.
Bake the patties for 15–20 minutes until brown.
To assemble, layer each bottom bun with arugula, a patty, pickled radishes, the top bun and a toothpick-speared petite pickle.
Pickled Radishes:
Combine first 3 ingredients in a clean 1 quart glass jar. Add vinegar, salt, and sugar. Cover; shake until sugar and salt begin to dissolve.
Refrigerate for at least 3 days, shaking once a day.
Notes
DO AHEAD: Can be made 1 month ahead. (The flavor mellows the longer the mixture pickles.) Keep chilled. Source: Epicurious