Note on cooking time: you may be able to reduce the total amount of time spent cooking if you cook some items concurrently.
Prepare aioli (you can do this ahead of time): place mayonnaise, cloves of garlic, fresh sage, olive oil, and fresh lemon juice in a small food processor or blender.
Blend until smooth and creamy; set aside.
Mix together ground meat, zucchini, beaten egg, sage, vinegar, garlic, salt and pepper.
Form into 4 patties and refrigerate on waxed paper until time to cook.
Peel sweet potatoes.
Using a food processor or mandolin, shave potatoes on the thinnest setting (they should be about as thin as a potato chip).
Heat oil to a depth of several inches in a large skillet or use a deep fryer.
Cook sweet potato shavings in small batches until they are crisp (about halfway through cooking you may press them against the side of the fryer a little bit to reduce their flat shape).
If you wish to bake your chips instead of frying them, place sweet potato shavings in a large plastic bag with several tablespoons of oil (just enough to coat) and shake bag gently until shavings are lightly covered with oil.
Place shavings on an oiled baking sheet and bake at 350F for about 20 minutes, then turn chips and bake another 10 minutes or so or until crispy (watch them so they don't burn).
Drain on paper toweling, and immediately season with salt and a sprinkling of cayenne pepper.
Heat 2 tablespoons butter and 1 tablespoon of oil in a large skillet.
Cook onion slices over medium-low heat until caramelized; keep warm until needed.
Grill patties over medium-hot coals (make sure to use a fine mesh grate and oil it thoroughly to reduce sticking) or cook in a large skillet or griddle for 7-8 minutes per side or until cooked through.
Plate burgers on toasted kaiser rolls with sage aioli, grilled onions, and a few sweet potato chips (or may have chips on the side).
Using cheese on your burgers is optional, but I would recommend a sharp cheddar if you go with that.
Any extra aioli may be refrigerated and used as a dip for crudites, cooked vegetables, etc.