  We reanalyze the experiment of Schmitt $\textit{et al.}$ on the
$^{10}$Be$(d,p)^{11}$Be transfer reaction [Phys. Rev. Lett. $\textbf{108}$,
192701 (2012)] by exploring the beam-energy and angular ranges at which the
reaction is strictly peripheral. We consider the adiabatic distorted wave
approximation (ADWA) to model the reaction and use a Halo-EFT description of
$^{11}$Be to systematically explore the sensitivity of our calculations to the
short-range physics of the $^{10}$Be-$n$ wave function. We find that by
selecting the data at low beam energy and forward scattering angle the
calculated cross sections scale nearly perfectly with the asymptotic
normalization coefficient (ANC) of the $^{11}$Be bound states. Following these
results, a comparison of our calculations with the experimental data gives a
value of $C_{1s1/2}=0.785\pm0.03$ fm$^{-1/2}$ for the $\frac{1}{2}^+$
ground-state ANC and $C_{0p1/2}=0.135\pm0.005$ fm$^{-1/2}$ for the
$\frac{1}{2}^-$ excited-state, which are in perfect agreement with the
$\textit{ab initio}$ calculations of Calci $\textit{et al.}$, who obtain
$C^{\textit{ab initio}}_{1/2^+}=0.786$ fm$^{-1/2}$ and $C^{\textit{ab
initio}}_{1/2^-}=0.129$ fm$^{-1/2}$ [Phys. Rev. Lett. $\textbf{117}$, 242501
(2016)].
