In a small saucepan, heat the water, sugar, vinegar, and salt. Place the onions in a heatproof bowl, cover with the vinegar mixture and cool to room temperature.
To make the aioli, combine all the ingredients in a small bowl. Stir well with a whisk.
To make the vinaigrette, combine all the ingredients other than the oil and fresh herbs in a blender or food processor. Purée until smooth. With the motor running, drizzle in the oil until emulsified. Fold in the herbs and season with salt and pepper.
Form the burger into 4 patties. Sprinkle with salt and pepper.
Heat the canola oil in a medium skillet over medium-high heat. Cook the patties for 4 minutes per side or until lightly browned and cooked through. Add a slice of cheese to each burger after flipping.
Toss the mixed greens with the harissa vinaigrette in a large bowl.
Serve the burgers on hamburger buns, topped with aioli and pickled onions, alongside salad.