  The currently unmeasured triple Higgs coupling is one of the strong
motivations for future physics programs at the LHC and beyond. A sufficiently
precise measurement can lead to qualitative changes in our understanding of
electroweak symmetry breaking and the cosmological history of the Higgs
potential. As such, the quantitative measurement of this coupling is now one of
the benchmark measurements for any proposed collider. We study the capability
of a potential $27\,\mathrm{TeV}$ HE-LHC upgrade in measuring the Higgs
trilinear coupling via the di-Higgs production process in the
$b\bar{b}\gamma\gamma$ channel. We emphasize that a key background from single
Higgs production via gluon fusion has been underestimated and underappreciated
in prior studies. We perform a detailed study taking into account two different
potential detector scenarios, and validate against HL-LHC projections from
ATLAS. We find that the di-Higgs production process can be observed at $\geq
4.5 \sigma$, corresponding to a $\sim 40\%$ measurement of the Higgs
self-coupling, with $15\,\mathrm{ab}^{-1}$ of data at the HE-LHC.
