Bring a large pot of salted water to a boil. Submerge the basil all at once for 30 seconds, then remove and run under cold water in a colander. Place in a blender, along with the shallot, garlic, olive oil and salt. Purée until smooth.
Cover the salmon with the sauce and marinate overnight or for at least 4 hours.
Preheat the oven to 400°F.
To make the succotash, heat the oil in a large skillet. Add the onions, garlic and both peppers and sauté for 3-4 minutes. Add the corn and stock and season with salt and pepper. Bring to a simmer for 10-15 minutes, until tender. Adjust seasoning and cool.
Place the salmon on a baking sheet, discarding marinade. Roast for 15-18 minutes, until cooked through.
When the succotash is cool, stir in the tomatoes and edamame.
Whisk together the vinaigrette ingredients in a small bowl or blender.
To serve, divide the salmon and succotash between plates. Top with vinaigrette.