Preheat the oven to 425°. On a rimmed baking sheet, drizzle the bread with 1 tsp. oil; season with salt and pepper and toss to coat. Spread out in a single layer and bake the croutons until golden and crispy, 8 to 10 minutes; transfer to a plate.
Preheat the broiler. In a small bowl, whisk 2 tsp. mustard and 1 tsp. vinegar. On a foil-lined baking sheet, arrange the salmon, skin side down. Brush with the mustard mixture; season. Broil until the fish is just opaque in the center, about 7 minutes. Let cool, then flake with a fork; discard the skin.
In a blender, puree the remaining 5 tbsp. oil, 2 tbsp. vinegar and 1 tsp. mustard with the red onion and 5 tbsp. water. Add the basil and blend until smooth; season.
On 4 plates, layer half the lettuce, radicchio, apple, salmon and croutons. Drizzle with half the dressing; season and repeat the layering with the remaining ingredients.