Executive control (EC) emerges in the first year of life, with the ability to inhibit prepotent responses (inhibitory control [IC]) and to flexibly readapt (cognitive flexibility [CF]) steadily improving. Simultaneously, electrophysiological brain activity undergoes profound reconfiguration, which has been linked to individual variability in EC. However, most studies exploring this relationship have used relative/absolute power and tasks that combine different executive processes. In addition, brain activity conflates aperiodic and oscillatory activity, which hinders the interpretation of the relationship between power and cognition. In the current study, we used the "Early Childhood Inhibitory Touchscreen Task" (ECITT) to examine the development of EC skills from 9 to 16 months in a longitudinal sample, and related performance of the task to resting-state EEG (rs-EEG) power, separating oscillatory and aperiodic activity. Our results showed improvement in IC but not in CF with age. In addition, alpha and theta oscillatory activity were concurrent (9-mo.) and longitudinal predictors of CF in toddlerhood, whereas the aperiodic exponent of the EEG signal did not contribute to EC. These findings demonstrate the relevance of oscillatory brain activity for cognitive development and provide an early brain marker for the early development of EC.