Results of broadband dielectric spectroscopy of flat micronic graphite (FMG)/polyurethane (PU) resin composites are presented in a wide temperature range (25–450 K). The electrical percolation threshold was found to lie between 1 and 2 vol. % of FMG. Above the percolation threshold, the composites demonstrated a huge hysteresis of properties on heating and cooling from room temperature up to 450 K, along with extremely high values of dielectric permittivity and electrical conductivity. Annealing proved to be a very simple but powerful tool for significantly improving the electrical properties of FMG-based composites. In order to explain this effect, the distributions of relaxation times were calculated by the complex impedance formalism. Below room temperature, both dielectric permittivity and electrical conductivity exhibited a very low temperature dependence, mainly caused by the different thermal properties of FMG and pure PU matrix.