Wood-based products are traditionally bonded with synthetic adhesives. Resources availability and ecological concerns have drawn attention to bio-based sources. The use of tannin-based adhesives for engineered wood products has been known for decades, however, these formulations were hardly used for the gluing of solid wood because their rigidity involved low performance. In this work, a completely bio-based formulation consisting of Quebracho (Schinopsis balancae) extract and furfural is characterized in terms of viscosity, gel time, and FT-IR spectroscopy. Further, the usability as an adhesive for beech (Fagus sylvatica) plywood with regard to press parameters (time and temperature) and its influence on physical (density and thickness) and mechanical properties (modulus of elasticity, modulus of rupture and tensile shear strength) were determined. These polyphenolic adhesives presented non-Newtonian behavior but still good spreading at room temperature as well as evident signs of crosslinking when exposed to 100 °C. Within the press temperature, a range of 125 °C to 140 °C gained suitable results with regard to mechanical properties. The modulus of elasticity of five layered 10 mm beech plywood ranged between 9600 N/mm2 and 11,600 N/mm2, respectively, with 66 N/mm2 to 100 N/mm2 for the modulus of rupture. The dry state tensile shear strength of ~2.2 N/mm2 matched with other tannin-based formulations, but showed delamination after 24 h of water storage. The proposed quebracho tannin-furfural formulation can be a bio-based alternative adhesive for industrial applicability for special plywood products in a dry environment, and it offers new possibilities in terms of recyclability.