  We present an algorithm for the simultaneous measurement of a pulse
time-of-arrival (TOA) and dispersion measure (DM) from folded wideband pulsar
data. We extend the prescription from Taylor (1992) to accommodate a general
two-dimensional template "portrait", the alignment of which can be used to
measure a pulse phase and DM. We show that there is a dedispersion reference
frequency that removes the covariance between these two quantities, and note
that the recovered pulse profile scaling amplitudes can provide useful
information. We experiment with pulse modeling by using a Gaussian-component
scheme that allows for independent component evolution with frequency, a
"fiducial component", and the inclusion of scattering. We showcase the
algorithm using our publicly available code on three years of wideband data
from the bright millisecond pulsar J1824-2452A (M28A) from the Green Bank
Telescope, and a suite of Monte Carlo analyses validates the algorithm. By
using a simple model portrait of M28A we obtain DM trends comparable to those
measured by more standard methods, with improved TOA and DM precisions by
factors of a few. Measurements from our algorithm will yield precisions at
least as good as those from traditional techniques, but is prone to fewer
systematic effects and is without ad hoc parameters. A broad application of
this new method for dispersion measure tracking with modern large-bandwidth
observing systems should improve the timing residuals for pulsar timing array
experiments, like the North American Nanohertz Observatory for Gravitational
Waves.
