The Cosmological Lithium Problem refers to the large discrepancy between the abundance of primordial 7Li predicted by the standard theory of Big Bang Nucleosynthesis and the value inferred from the so-called “Spite plateau” in halo stars. A possible explanation for this longstanding puzzle in Nuclear Astrophysics is related to the incorrect estimation of the destruction rate of 7Be, which is responsible for the production of 95% of primordial Lithium. While charged-particle induced reactions have mostly been ruled out, data on the 7Be(n,alpha) and 7Be(n,p) reactions are scarce or completely missing, so that a large uncertainty still affects the abundance of 7Li predicted by the standard theory of Big Bang Nucleosynthesis. Both reactions have been measured at the n TOF facility at CERN, providing for the first time data in a wide neutron energy range.