The macro- and microstructural characteristics of sleep electroencephalography have been associated with several aspects of executive functioning. However, only a few studies have addressed the association of sleep characteristics with the learning involved in the acquisition of executive functions, and no study has investigated this for planning and problem-solving skills in the developing brain of children. The present study examined whether children's sleep stages and microstructural sleep characteristics are associated with performance improvement over repeated assessments of the Tower of Hanoi task, which requires integrated planning and problem-solving skills. Thirty children (11 boys, mean age 10.7 years, SD = 0.8) performed computerized parallel versions of the Tower of Hanoi three times across 2 days, including a night with polysomnographically assessed sleep. Pearson correlations were used to evaluate the associations of Tower of Hanoi solution time improvements across repeated assessments with sleep stages (% of total sleep time), slow-wave activity, and fast and slow spindle features. The results indicated a stronger performance improvement across wake in children with more Stage N2 sleep and less slow-wave sleep. Stronger improvements across sleep were present in children in whom slow spindles were more dense, and in children in whom fast spindles were less dense, of shorter duration and had less power. The findings indicate that specific sleep electroencephalography signatures reflect the ability of the developing brain to acquire and improve on integrated planning and problem-solving skills.