Meditation practice is believed to foster states of mindful awareness and mental quiescence in everyday life. If so, then the cultivation of these qualities with training ought to leave its imprint on the activity of intrinsic functional brain networks. In an intensive longitudinal study, we investigated associations between meditation practitioners' experiences of felt mindful awareness and changes in the spontaneous electrophysiological dynamics of functional brain networks. Experienced meditators were randomly assigned to complete 3 months of full-time training in focused-attention meditation (during an initial intervention) or to serve as waiting-list controls and receive training second (during a later intervention). We collected broadband electroencephalogram (EEG) during rest at the beginning, middle, and end of the two training periods. Using a data-driven approach, we segmented the EEG into a time series of transient microstate intervals based on clustering of topographic voltage patterns. Participants also provided daily reports of felt mindful awareness and mental quiescence, and reported daily on four experiential qualities of their meditation practice during training. We found that meditation training led to increases in mindful qualities of awareness, which corroborate contemplative accounts of deepening mental calm and attentional focus. We also observed reductions in the strength and duration of EEG microstates across both interventions. Importantly, changes in the dynamic sequencing of microstates were associated with daily increases in felt attentiveness and serenity during training. Our results connect shifts in subjective qualities of meditative experience with the large-scale dynamics of whole brain functional EEG networks at rest.