Start by making the sauce. Place the guar gum in a small bowl and stir in the avocado oil until mixed. Set aside.
Put the eggs, Dijon mustard, and sea salt in the bottom of the jug that came with your stick blender, or a tall mason jar slightly wider than the whisk of the stick blender.
Holding the blender in one hand make sure the bottom of blender is in contact with the bottom of the jar and turn on to mix the ingredients.
With the other hand, slowly pour the avocado oil mixed with guar gum into the jar while the blender is running.
Once all the oil has been added, continue blending until the ingredients at the bottom turn thick and creamy. Then slowly, with the blender still running, raise the stick blender up the jar. Blend until all of the mayonnaise is thick and creamy.
Add the pickle juice, white vinegar, onion powder, and paprika and blend until thoroughly combined.
Very finely chop the dill pickles and stir into the sauce. Cover with plastic wrap and store in the fridge until ready to serve.
To make the salad, cook the burgers using your favorite method. When cool, slice into “fingers.”
Slice the cheese into narrow slices.
Chop the onion.
Dry toast the sesame seeds in a pan over a low heat until golden brown, moving them continuously so they don’t burn.
Thinly slice the 4-inch pickles.
Shred the heads of lettuce by slicing very thinly across the lettuce.
Place the shredded lettuce in a large serving bowl, sprinkle over the chopped onion, top with pickle slices, cheese, sliced burgers, and finally sprinkle with toasted sesame seeds.
Spoon the sauce over the salad or serve on the side.