Multilayer packaging is an important part of the packaging market, but it is not recyclable with conventional methods since it is made of different thermodynamically immiscible materials. In this work, it was shown that it is possible to produce a PET//LDPE laminate in a pilot plant for lamination by using an adhesive consisting of maleimide- and furan-functionalized polyurethane prepolymers that cure through the Diels–Alder reaction. The material could then be delaminated in a small-scale recycling plant using a solvent-based recycling process by partially opening the Diels–Alder adducts through the influence of temperature. The PET and LDPE could be recovered without any adhesive residues before each material was regranulated, and in the case of the PE, a film was produced via cast film extrusion. The obtained PET granulate exhibited a slight, approximately 10%, decrease in molecular weight. However, since small amounts of LDPE could not be separated, compatibilization would still be required here for further use of the material. The obtained LDPE film was characterized by means of infrared spectrometry, differential scanning calorimetry, tensile testing, determination of the melt index, and molecular weight. The film showed lower crosslinking than usual for LDPE recycling and exhibited good mechanical properties. In this work, it was thus shown that upscaling of the laminate production with the modified adhesive and also its recycling at the pilot plant scale is possible and thus could be an actual option for recycling multilayer packaging.