  We consider the simultaneous production of two heavy-flavoured hadrons -
particularly D mesons - at the LHC. We base our calculations on collinearly
factorized QCD at next-to-leading order, using the contemporary parton
distribution functions and D-meson fragmentation functions. The contributions
of double-parton scatterings are included in the approximation of independent
partonic interactions. Our framework benchmarks well with the available
proton-proton data from the LHCb collaboration giving us confidence to make
predictions for proton-lead collisions. Our results indicate that the double
D-meson production in proton-lead collisions should be measurable at the LHCb
kinematics with the already collected Run-II data, and should provide evidence
for double-parton scattering at perturbative scales with a nuclear target.
