Combine first 3 ingredients in a small bowl, stirring to dissolve salt and sugar. Stir in onion. Let stand at room temperature for at least 1 hour, stirring occasionally, or refrigerate up to 3 days.

Combine turkey, eggs, salt, and pepper to taste in a large bowl. Form into 8 (4 inch) patties. Place on a plate or small tray, cover and refrigerate at least one hour and up to overnight.

Combine avocado, cumin, ancho chile powder, garlic, and salt and pepper to taste in a medium bowl, gently mashing with a fork. Stir in juice of 1 lime. Fold in tomato. Cover with plastic wrap, pressing it into the surface of the guacamole to prevent browning, and refrigerate. Preheat grill to medium-high. Oil grill.

Brush patties with oil and place on grill. Cover and cook 8-10 minutes or until done, turning once. Top each patty with 1 slice of cheese. Cover and cook 15 seconds or until cheese starts to melt. Transfer burgers to a plate and keep warm.

Warm tortillas on grill. Lay tortillas on a work surface. Lay 1 burger on top half of tortilla (at the 12 o'clock position). Top each burger with pickled onions, sprouts and guacamole. Drizzle with hot sauce. Fold the bottom half of the tortilla up to cover the burger, then lift to fold the sides under the burger to form an envelope. Cut remaining lime into 8 wedges. Serve burgers with lime wedges.