Want to make this recipe ahead? Cut the vegetables and refrigerate in separate airtight containers (line vegetables with damp paper towels), for up to one day.
Make brown sauce: In a large bowl, whisk together oyster sauce, vinegar, and sesame oil until combined; season with salt.
In a large pot fitted with a steamer basket, bring 1 inch of water to a boil over medium-high heat. Add broccoli to basket in a single layer. Cover; steam until crisp-tender, about 2 minutes.
Scatter snow peas on top of broccoli in an even layer; cover, and continue steaming until snow peas are bright green, about 1 minute more. Add broccoli and snow peas to bowl with sauce; toss to coat. Serve immediately.