The transconductance gₘ = dI_D/dV_G of a field-effect transistor (FET) is conventionally read as a proxy for carrier density. We show that it is instead a spectroscopic probe of the carrier distribution: because gₘ weights the spectral current j(E) by the gate-voltage derivative ∂ f(E)/∂ V_G and integrates over energy, it is sensitive to the shape of f(E), not merely its integrated weight n. We develop an energy-resolved transport framework for two-dimensional (2D) FETs and, within a gate-independent spectral-kernel approximation, derive the decomposition gₘ = gₘ⁽ⁿ⁾ + gₘ^((α)) into the conventional density-modulation term gₘ⁽ⁿ⁾ and a distribution-shape-driven term gₘ^((α)). The latter, obtained as the residual after subtracting the smooth density-modulation background from the measured gₘ, exhibits a characteristic anomalous peak at a gate voltage V_G^(rm pk). This peak has no counterpart in equilibrium transport and cannot be explained by carrier density modulation alone. With the spectral kernel calibrated, the peak position and height – extracted from standard DC/lock-in gₘ sweeps – constrain the hot-carrier energy E₀, spectral width σ, and generation threshold n_c, realizing a steady-state, all-electrical spectroscopy of the carrier distribution. An optional time-resolved extension further recovers the carrier relaxation time τ from the transient response following a pump excitation, establishing the 2D FET as a distribution-function spectrometer that requires no optical readout.