COVID-19 has got us to face a new situation where, for the lack of ready-to-use vaccines, it is necessary to support vaccination with complex non-pharmaceutical strategies. In this paper, we provide a novel Mixed Integer Nonlinear Programming formulation for fine-grained optimal intervention planning (i.e., at the level of the single day) against newborn epidemics like COVID-19, where a modified SIR model accounting for heterogeneous population classes, social distancing and several types of vaccines (each with its efficacy and delayed effects), allows us to plan an optimal mixed strategy (both pharmaceutical and non-pharmaceutical) that takes into account both the vaccine availability in limited batches at selected time instants and the need for second doses while keeping hospitalizations and intensive care occupancy below a threshold and requiring that new infections die out at the end of the planning horizon. In order to show the effectiveness of the proposed formulation, we analyze a case study for Italy with realistic parameters.