A resin infusion method that incorporates a melt-on-demand approach. The method includes: (a) providing a curable resin composition in the form of a block of frozen resin (20); (b) coupling the blockof frozen resin (20) to an inlet port of a heated extruder (22), which comprises at least one rotating screw (24) housed within a heated barrel (25); (c) progressively melting the block of frozen resin (20) at the inlet port and concurrently feeding the melt resin through the heated barrel (25) to produce a liquid resin having a viscosity suitable for resin infusion; (d) continuously feeding the liquid resin exiting from the extruder to a mold, which contains a fibrous preform; and (e) introducing the liquid resin into the fibrous preform, wherein the block of frozen resin (20) provides an amount of resin composition sufficient for infusing the entire fibrous preform.