  The Vera C. Rubin Observatory's Legacy Survey of Space and Time is forecast
to collect a large sample of Type Ia supernovae (SNe Ia) that could be
instrumental in unveiling the nature of Dark Energy. The feat, however,
requires measuring the two components of the Hubble diagram - distance modulus
and redshift - with a high degree of accuracy. Distance is estimated from SNe
Ia parameters extracted from light curve fits, where the average quality of
light curves is primarily driven by survey parameters such as the cadence and
the number of visits per band. An optimal observing strategy is thus critical
for measuring cosmological parameters with high accuracy. We present in this
paper a three-stage analysis aiming at quantifying the impact of the Deep
Drilling (DD) strategy parameters on three critical aspects of the survey: the
redshift completeness (originating from the Malmquist cosmological bias), the
number of well-measured SNe Ia, and the cosmological measurements. Analyzing
the current LSST survey simulations, we demonstrate that the current DD survey
plans are characterized by a low completeness ($z~\sim$ 0.55-0.65), and
irregular and low cadences (few days) that dramatically decrease the size of
the well-measured SNe Ia sample. We then propose a modus operandi that provides
the number of visits (per band) required to reach higher redshifts. The results
of this approach are used to design a set of optimized DD surveys for SNe Ia
cosmology. We show that most accurate cosmological measurements are achieved
with Deep Rolling surveys characterized by a high cadence (one day), a rolling
strategy (each field observed at least two seasons), and two sets of fields:
ultra-deep ($z \gtrsim 0.8$) and deep ($z \gtrsim 0.6$) fields. We also
demonstrate that a deterministic scheduler including a gap recovery mechanism
is critical to achieve a high quality DD survey required for SNe Ia cosmology.
