In this work, a novel sustainable approach was proposed for the integral valorisation of Arctium lappa (burdock) seeds and roots. Firstly, a preliminary recovery of bioactive compounds, including unsaturated fatty acids, was performed. Then, simple sugars (i.e., fructose and sucrose) and phenolic compounds were extracted by using compressed fluids (supercritical CO2 and propane). Consequently, a complete characterisation of raw biomass and extraction residues was carried out to determine the starting chemical composition in terms of residual lipids, proteins, hemicellulose, cellulose, lignin, and ash content. Subsequently, three alternative ways to utilise extraction residues were proposed and successfully tested: (i) enzymatic hydrolysis operated by Cellulases (Thricoderma resei) of raw and residual biomass to glucose, (ii) direct ethanolysis to produce ethyl levulinate; and (iii) pyrolysis to obtain biochar to be used as supports for the synthesis of sulfonated magnetic iron-carbon catalysts (Fe-SMCC) to be applied in the dehydration of fructose for the synthesis of 5-hydroxymethylfurfural (5-HMF). The development of these advanced approaches enabled the full utilisation of this resource through the production of fine chemicals and value-added compounds in line with the principles of the circular economy.