  IceCube has observed 80 astrophysical neutrino candidates in the energy range
0.02 < E_\nu/PeV < 2. Deep inelastic scattering of these neutrinos with
nucleons on Antarctic ice sheet probe center-of-mass energies $\sqrt{s} \sim$ 1
TeV. By comparing the rates for two classes of observable events, any departure
from the benchmark (perturbative QCD) neutrino-nucleon cross section can be
constrained. Using the projected sensitivity of South Pole next generation
neutrino telescope we show that this facility will provide a unique probe of
strong interaction dynamics. In particular, we demonstrate that the high-energy
high-statistics data sample to be recorded by IceCube-Gen2 in the very near
future will deliver a direct measurement of the neutrino-nucleon cross section
at $\sqrt{s} \sim 1$ TeV, with a precision comparable to perturbative QCD
informed by HERA data. We also use IceCube data to extract the neutrino-nucleon
cross section at $\sqrt{s} \sim 1$ TeV through a likelihood analysis,
considering (for the first time) both the charged-current and neutral-current
contributions as free parameters of the likelihood function.
