Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions1. These techniques, such as photoemission and tunnelling, yield measurements of the 'single-particle' density of states spectrum of a system2. This density of states is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy, and is among the most fundamental and directly calculable quantities in theories of highly interacting systems3. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect4, has proved difficult to probe spectroscopically. Here we present an improved version of time-domain capacitance spectroscopy5 that allows us to measure the single-particle density of states of a 2DES with unprecedented fidelity and resolution. Using the method, we perform measurements of a cold 2DES, providing direct measurements of interesting correlated electronic effects at energies that are difficult to reach with other techniques; these effects include the single-particle exchange-enhanced spin gap6, single-particle lifetimes7 in the quantum Hall system, and exchange splitting of Landau levels not at the Fermi surface.