Place a rimmed baking sheet in the upper third of the oven; preheat to 450˚ F. Toss the cauliflower and potatoes with the olive oil, curry powder, 1/2 teaspoon salt and a few grinds of pepper in a large bowl. Spread out the vegetables on the hot pan, cut-sides down, and bake until browned around the edges and tender, 25 to 30 minutes.
Meanwhile, combine the yogurt, cucumber, cilantro, 1 scallion, the lemon juice, coriander, red pepper flakes and a big pinch of salt in a small bowl. Stir to combine, then refrigerate until ready to use.
Remove the pan from the oven and preheat the broiler. Stir the cauliflower and potatoes, then arrange them to create four spots for the salmon. Add the salmon to the pan, skin-side down, and season with salt and the paprika. Combine the chutney and vinegar and spread over the top of the fish. Broil until the salmon is browned around the edges and just cooked through, 6 to 9 minutes, depending on the thickness.
Spoon some of the yogurt sauce over the salmon. Top with the remaining 2 scallions and cilantro; sprinkle with paprika. Serve with the remaining yogurt sauce.