Solid state electrolytes are a promising alternative to flammable liquid electrolytes for high-energy lithium battery applications. In this work polymer-ceramic composite electrolyte membrane with high ceramic loading (greater than 60 vol%) is fabricated using a model polymer electrolyte poly(ethylene oxide) + lithium trifluoromethane sulfonate and a lithium-conducting ceramic powder. The effects of processing methods, choice of plasticizer and varying composition on ionic conductivity of the composite electrolyte are thoroughly investigated. The physical, structural and thermal properties of the composites are exhaustively characterized. We demonstrate that aqueous spray coating followed by hot pressing is a scalable and inexpensive technique to obtain composite membranes that are amazingly dense and uniform. The ionic conductivity of composites fabricated using this protocol is at least one order of magnitude higher than those made by dry milling and solution casting. The introduction of tetraethylene glycol dimethyl ether further increases the ionic conductivity. The composite electrolyte's interfacial compatibility with metallic lithium and good cyclability is verified by constructing lithium symmetrical cells. A remarkable Li+ transference number of 0.79 is discovered for the composite electrolyte.