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.