The peak window, and the one most people choose for good reason. All road passes are open, every sector is accessible, and the days run from 5am light to 8pm dark. Temperatures in Leh sit between 15°C and 25°C through the day, dropping to 5–10°C at night — pleasant in town, considerably colder at the passes. At Khardung La in August, you'll want a down jacket regardless of what the Leh afternoon felt like.
August is what we'd recommend for a first visit. The monsoon affects the rest of India but Ladakh sits in a rain shadow — you'll see dramatic clouds and the occasional brief shower, but nothing that shuts down itineraries. The passes are at their most reliable. The Hemis Festival — masked dances, monks, one of the oldest monasteries in the region — falls in June or July, depending on the Tibetan lunar calendar; if the dates align when you're planning, build around it.
