Prepare broccoli: Cut off and discard tough ends of stalks, leaving about 2 inches attached to the florets. Using a paring knife, cut broccoli lengthwise into pieces. With a sturdy vegetable peeler (or sharp knife), peel away the tough outer layer from the stalks. In a large pot fitted with a steamer basket, bring 1 inch of water to a boil. Add broccoli pieces in a single layer. Cover, and steam until tender, about 5 minutes.
Meanwhile, in a large bowl, whisk together lime juice and sesame oil; season with salt.
Add broccoli to dressing; toss lightly to coat. Serve immediately.