This article investigates factor-augmented sparse MIDAS (Mixed Data Sampling) regressions for high-dimensional time series data, which may be observed at different frequencies. Our novel approach integrates sparse and dense dimensionality reduction techniques. We derive the convergence rate of our estimator under misspecification, $\tau$-mixing dependence, and polynomial tails. Our method's finite sample performance is assessed via Monte Carlo simulations. We apply the methodology to nowcasting U.S. GDP growth and demonstrate that it outperforms both sparse regression and standard factor-augmented regression during the COVID-19 pandemic. To ensure the robustness of these results, we also implement factor-augmented sparse logistic regression, which further confirms the superior accuracy of our nowcast probabilities during recessions. These findings indicate that recessions are influenced by both idiosyncratic (sparse) and common (dense) shocks.