Construction of thin thickness and broadband microwave absorption materials (MAMs) is challenging but important. One important and relatively successful strategy involves the reduction of quarter-wavelength resonance thickness by increasing permittivity (εr) and permeability (μr). In this study, MOFs-derived core-shell structured flaky carbonyl iron/Co@C (FCI/Co@C) composites were synthesized via self-polymerization and in-situ pyrolysis to enhance εr. The effects of Co content in the porous carbon shell on the microstructure and electromagnetic performance of the FCI/Co@C composites were investigated. The FCI/Co@C composite with a Co-to-Zn molar ratio of 1:0 and 3:1 in its precursor and 70 wt% of filler exhibited excellent microwave absorption performance. The effective absorption bandwidth (EAB, corresponding to a reflection loss of less than −10 dB) of FCI/Co@C-1 reached 5.7 GHz (12.3–18 GHz) with a thickness of 1.28 mm, while the EAB of FCI/Co@C-3/1 reached 5.2 GHz (12.8–18 GHz) with a thickness of 1.19 mm, and both samples demonstrated broadband absorption in the Ku band. Thus, core-shell structured FCI/Co@C composites can be used as thin broadband MAMs in the Ku band. Furthermore, this work not only provides a simple method for constructing FCI-based core-shell structured MAMs, but also offers a novel strategy for reducing thickness while maintaining good microwave absorption performance.