Traditional autoclave cured carbon fiber (CF) composites are cost, equipment, and energy-intensive. Frontally polymerizable composites based on catalyzed dicyclopentadiene (DCPD) resins have previously been shown to provide a low energy and rapid means for out-of-autoclave curing of structural composites. Previous efforts on the Vacuum-Assisted Resin Transfer Molding processing and thermal initiation under applied pressure yielded high-quality composite panels. However, like many composite processes, the panel dimensions were smaller than the size of the tooling. In this work, we develop a rapid and continuous manufacturing technique involving through-thickness curing of the frontally polymerizable resin to fabricate CF-reinforced structural beams with dimensions exceeding that of the processing equipment. The beams are fabricated through a continuous process where plies of uncured DCPD/CF lamina are fed into a pair of hot rollers for simultaneous compaction and curing. We investigate the effects of lamination speed, temperature, and pressure on the degree of cure of the composites and identify proper combinations of these parameters to manufacture fully cured unidirectional and cross-ply laminates. The laminates have high fiber volume fractions, low void contents, and minimal geometric variations. The process can be made continuous but is initially demonstrated for composite beams with ~300 mm lengths at a rate of 0.72 m/min. This is more than three times longer than the length of the low-cost fabricator (~100 mm), orders of magnitude faster than traditional composite processing, and has many attractive attributes for manufacturing of high-performance composites in austere or energy-constrained environments like space or remote locations.