Preheat a grill to medium high. Season the salmon with salt and pepper. Combine the paprika, brown sugar, cumin and garlic powder in a small bowl. Rub the spice mix all over the salmon and set aside. Toast the almonds in a small skillet over medium heat, swirling the skillet, 4 to 6 minutes. Transfer to a plate.
Combine 1/4 cup toasted almonds, the roasted red peppers, vinegar and 1 tablespoon water in a blender. Puree until mostly smooth. With the machine running, slowly add 1/4 cup olive oil and puree until smooth; season with salt and pepper.
Oil the grill grates. Toss the beans with the remaining 2 teaspoons olive oil; season with salt and pepper. Put in a grill basket and grill, tossing occasionally, until charred and tender, 8 to 10 minutes. Rub the salmon with olive oil and grill until well-marked, 3 to 4 minutes per side for medium doneness.
Toss the beans with the basil and divide among plates. Sprinkle with the remaining almonds. Add the salmon to the plates and top with the sauce.