For the salmon: Preheat the oven to 250 degrees F.
Brush a baking dish with a thin coat of softened butter and sprinkle a little salt and pepper over the surface. Set the salmon fillets upright (flat-side down) on the baking dish, brush a little soft butter over each fillet and sprinkle them with salt and pepper.
In a small bowl, whisk the pesto, mustard and lemon juice together and season it with salt and pepper. Spoon the mixture evenly over the salmon, covering the top surface only. Bake until the desired doneness, 8 to 10 minutes for medium rare for 1 1/2-inch-thick fillets (cook longer for thicker pieces).
For the salad: Meanwhile, put the cucumber into a clean towel on a cutting board and smash it with the heel of your hand. Unwrap the cucumber and slice it crosswise into 1/2-inch pieces; transfer them to a mixing bowl and sprinkle a little salt over them. Add the dates and apples and stir to mix. Add the pine nuts, olive oil, mint and lemon juice; season with salt and pepper, and toss until evenly combined.
Serve the salmon fillets on warm plates with the salad on the side.