In a small bowl, whisk together the minced ginger, garlic, sesame oil, rice wine vinegar, soy sauce, chili paste, and honey until the mixture is smooth and well combined. The honey will help emulsify the dressing slightly. Set aside while you prepare the vegetables—the flavors will continue to meld as it sits.
Fill a large bowl with ice and cold water—this will be essential for stopping the cooking process and keeping the vegetables vibrant and crisp. Simultaneously, bring a pot of salted water to a rolling boil over high heat. I find that having both ready before cooking makes the timing much smoother and prevents any vegetables from overcooking.
Add the shelled edamame to the boiling water and cook for 3 minutes. In the final 30 seconds, add the trimmed snap peas and cook together for the remaining time—this staggers the cooking so both vegetables finish at the same moment with proper texture. Immediately drain both vegetables in a colander.
Immediately transfer the drained edamame and snap peas to the prepared ice bath and let them sit for 5 minutes. This stops the cooking process and sets their bright green color while maintaining their crisp texture. Drain thoroughly and pat dry with paper towels to remove excess moisture, which would dilute your dressing.
In a large bowl, combine the dried edamame and snap peas with the shredded carrots. Pour the dressing from Step 1 over the vegetables and toss gently but thoroughly to coat everything evenly. The vegetables will stay crisp because they've been properly dried—I always make sure to pat them completely dry to avoid a watery salad.
Transfer the dressed salad to a serving platter or individual bowls and sprinkle with toasted sesame seeds just before serving. This keeps the seeds from softening and losing their nutty crunch.