Structuring wheat gluten proteins into gels with tunable mechanical properties would provide more versatility for the production of plant protein-rich food products. Gluten, a strongly elastic protein material insoluble in water, is hardly processable. We use a novel fractionation procedure allowing the isolation from gluten of a water/ethanol soluble protein blend, enriched in glutenin polymers at an unprecedented high ratio (50%). We investigate here the viscoelasticity of suspensions of the protein blend in a water/ethanol (50/50 v/v) solvent, and show that, over a wide range of concentrations, they undergo a spontaneous gelation driven by hydrogen bonding. We successfully rationalize our data using percolation models and relate the viscoelasticity of the gels to their fractal dimension measured by scattering techniques. The gluten gels display self-healing properties and their elastic plateaus cover several decades, from 0.01 to 10,000 Pa. In particular very soft gels as compared to standard hydrated gluten can be produced.