Cook quinoa & potatoes: Peel sweet potatoes, then cut into 1-inch pieces. Place quinoa in a small saucepan; add sweet potatoes, 1¼ cups water, and ½ teaspoon salt. Bring to a boil. Reduce heat to a simmer, cover, and cook until quinoa and sweet potatoes are tender and liquid is absorbed, about 17 minutes. Coarsely mash and spread on a plate to cool slightly.
Prep ingredients: Preheat the oven to 250°F. Trim ends from onion, then halve, peel and finely chop ½ cup; thinly slice the rest. Peel and thinly slice 1 large clove garlic. Holding core ends of Brussels sprouts, thinly slice crosswise and discard core ends. Squeeze a few times with your hands to separate leaves slightly.
Make cakes: Beat 1 large egg in a medium bowl; add chopped onion, ½ teaspoon salt, ¼ teaspoon pepper, quinoa-sweet potato mixture, and ½ cup of the panko, and stir to combine. Put remaining panko onto a plate and season with salt. Form the mixture into 4 cakes, each about 3-inches wide. Coat in panko.
Fry cakes: Heat ⅛-inch oil in a large skillet over medium-high. Add cakes and cook, turning once, until golden and crisp, 6–8 minutes. Drain on a paper towel lined baking sheet. Sprinkle with salt. Transfer to the oven to keep warm. Pour off oil and wipe out skillet.
Make sauce: In a small bowl, whisk mustard with sour cream, 1 teaspoon vinegar, and 1 teaspoon water. Season with salt and pepper.
Sauté Brussels sprouts: Heat 1 tablespoon oil over high. Add sliced onion and cook until golden, about 4 minutes. Add Brussels sprouts, garlic, salt and pepper to taste, cook until softened, about 2 minutes. Add remaining vinegar and ¼ cup water, cover, and cook 1 minute. Place quinoa-sweet potato cakes on plates, with Brussels sprouts and sauce served alongside for dipping