Pat the salmon with paper towels to blot it, especially the skin. Preheat your oven to broil.
Season the skin with salt & pepper and rub 1 tablespoon of olive oil all over the skin. Place the salmon on a broiler pan skin side up and broil for 10 minutes per inch of thickness. Pull out then pan and check that the salmon is cooked just through to the bottom and the skin is browned, crispy, and bubbling.
Meanwhile, shave the radishes and cucumbers lengthwise on a Japanese mandolin into a bowl with the whole herb leaves. Then cut the snap peas at a sharp angle into very thin slivers. Mince the garlic and macerate with a pinch of salt in the vinegar. Stir the additional 3 tablespoons of olive oil and the dried mint into the yogurt then stir in the garlic-vinegar mixture.
Pull the skin off the cooked salmon and slice 1/2 of it up into thin shards. Place the salmon lightly flaked into chunks onto a serving platter. Drizzle some of the yogurt dressing over the fish then gently toss the salad ingredients with the remainder of the dressing. Place on top of the salmon and serve.