  We present next-to-leading order (NLO) perturbative-QCD calculations of the
cross sections for $\ell N\to h X$ and $\ell N\to \mathrm{jet}\, X$. The main
feature of these processes is that the scattered lepton is not observed, so
that the hard scale that makes them perturbative is set by the transverse
momentum of the hadron or jet. Kinematically, the two processes thus become
direct analogs of single-inclusive production in hadronic collisions which, as
has been pointed out in the literature, makes them promising tools for
exploring transverse spin phenomena in QCD when the incident nucleon is
transversely polarized. We find that the NLO corrections are sizable for the
spin-averaged cross section. We also investigate in how far the scattering is
dominated by the exchange of almost real (Weizs\"{a}cker-Williams) photons. We
present numerical estimates of the cross sections for present-day fixed target
experiments and for a possible future electron ion collider.
