Prepare grill with a medium fire for direct-heat cooking. In a small bowl, combine aioli ingredients. Reserve 2 tablespoons for burgers and chill remainder until serving time.
Combine soy sauce, honey, and rice vinegar in a small, heavy saucepan. Mix cornstarch and 1 tablespoon wine in a small bowl until smooth and add to soy mixture. Place over grill and stir mixture until glaze boils and thickens slightly, about 3 minutes. Meanwhile, sip a glass of Sutter Home Sauvignon Blanc, saving remainder for grilling. Set glaze aside. In a large bowl, whisk together egg, aioli, sour cream, lime juice, and chili sauce. Stir in salmon, onion, mint, bread crumbs, and salt to combine. Coat hands with vegetable oil and form 4 patties. Brush grill with vegetable oil and grill patties until browned on bottom, about 3 minutes. Turn patties and brush cooked side with soy glaze. Cook 3 minutes, turn, and brush other side with glaze. Grill just until done, about 4 to 6 minutes, turning and brushing with glaze frequently. During the last few minutes of cooking toast buns, cut side down, on outside of grill. Place cucumber strips on bottom half of bun, top with burgers, aioli, and bun tops. Garnish with sprouts, if desired.