Every standard Jimmy John's sandwich contains soybean oil because both breads and the default mayo carry it, but the meats, cheeses and vegetables are clean and the Unwich lettuce wrap is an official way to order around the bread entirely.
Jimmy John's publishes a full ingredient statement for every component through its own ingredient search, so this is high confidence. Of 84 food components, 35 contain a named seed oil and 36 contain an additive from our watchlist. The problem is where the oil sits: both breads carry soybean oil (French Bread and Wheat Sub Bread) and the default Hellmann's Mayo is soybean oil, so every standard sandwich has it. The French Bread also carries calcium propionate, ammonium chloride and calcium peroxide as dough conditioners. What saves them is that the meats, cheeses and vegetables are genuinely clean - the turkey statement is turkey breast, turkey broth, salt, dextrose, tapioca starch, yeast extract, sea salt, citrus extract and natural flavor - and the Unwich lettuce wrap is an official, chain-wide way to order with no bread at all.