In a saucepan, stir together the sugar, orange juice, lemon juice, and salt. Bring to a boil, then reduce heat to low and simmer for three minutes, until the sugar dissolves. Turn off the heat. Stir in 1/2 cup oil, ginger, and garlic (if using). Let cool.

Pour into a dish or zip-top bag. Add the chicken and marinate at least two hours and up to overnight. Meanwhile, soak the skewers in water for one hour.

Thread the chicken onto the skewers. Make sure the chicken isn’t too wet (to avoid hot oil splatters during cooking). In a skillet, heat the remaining two tablespoons oil over high heat. Sear the chicken for two to three minutes per side, adding more oil if needed. Set aside.

In a deep container with high sides, use an immersion blender to combine the eggs, lemon juice, sugar, and salt. With the immersion blender running, slowly drizzle in the oil. Continue blending until the mixture turns into mayonnaise.

Set aside one cup mayonnaise and transfer the rest to another container, reserving it for other uses (see note). Return the one cup mayonnaise to the container with high sides. Add the avocado and horseradish, and blend until fully combined.

In a bowl, whisk together the oil, orange juice, lemon juice, salt, and pepper. Add kohlrabi and apples and toss to coat evenly. Sprinkle with pecans.

Place one heaping tablespoon aioli in the center of each plate and spread it out a bit with the back of a spoon. Add skewers on top and slaw on the side.