I don't think you really need much of a recipe to be honest, it's rather straight forward just by looking at it.
Of course it's not going to taste exactly the same because their meat patties contain a bunch of other chemicals and flavor enhancers in them that is not practical to recreated at home. These give their burgers their signature smell, but even without that enhancement you can make something fairly close.
I believe the "secret sauce" on the Big Mac is nothing more than a mixture of mayo, ketchup and sweet pickle relish - much like a Thousand Island dressing. Then you would need some shredded Romaine lettuce, a couple slices of American Cheese, and your burger buns, with the extra bottom bun or the "heel" which I believe it's referred to as.
Lightly butter and toast your buns, then add the sauce mixture to them along with the shredded lettuce. Melt the cheese over the burger patties, then assemble it all. I cannot recall if there are dill pickle slices on it or not, but if so add those too.