Preheat the oven to 425 degrees F. Line a baking sheet with aluminum foil. Bring a medium pot of heavily salted water to a boil. Fill a medium bowl with ice water and set aside.
Add the basil leaves, 2 tablespoons olive oil, 1 teaspoon shichimi togarashi, lemon zest, garlic, 1 teaspoon salt and a few grinds of pepper to a food processor and process until finely chopped, scraping down the sides of the bowl as needed. Transfer to a small bowl and fold in the panko.
Place the salmon fillets skin-side down on the prepared baking sheet and brush the tops with 2 tablespoons honey. Press the breadcrumb mixture all over the tops of each fillet (about 1 tablespoon per fillet). Bake until the breadcrumbs are golden brown and the salmon is firm and flakes easily when pressed, 12 to 15 minutes.
Meanwhile, place the pine nuts in a single layer in a small nonstick skillet and cook, shaking frequently, until they’re golden brown and smell nutty, 3 to 5 minutes. Transfer to a plate to cool.
Add the sugar snap peas to the boiling water and cook until very bright green and crisp tender, 1 to 2 minutes. Use a slotted spoon to immediately transfer the peas to the ice water to stop the cooking. Drain the snap peas, then cut them into thirds on a deep bias.
Put the lemon juice, mustard, vinegar, fish sauce, shallots, 1/4 teaspoon salt, a few grinds of pepper, the remaining 1 tablespoon of honey and the remaining pinch of shichimi togarashi in a large bowl. Use an immersion blender to mix and drizzle in the vegetable oil and the remaining 1 tablespoon of olive oil until all the ingredients are emulsified.
Fold in the snap peas until coated. Fold in the parsley leaves, toasted pine nuts and basil stems and serve alongside the salmon.