Put a rimmed baking sheet in the upper third of the oven; preheat to 475 degrees F. Add the shallots, drizzle with 1 tablespoon melted butter and season with salt; spread in a single layer. Roast until softened and starting to brown, 5 to 7 minutes.
Meanwhile, butterfly the shrimp: Peel the shrimp; make a deep cut down the center of the shrimp's back from head to tail without cutting all the way through. Remove the vein with the tip of the knife. Open the shrimp along the cut so it lies flat. Transfer to a large bowl.
Combine the remaining 5 tablespoons melted butter, the ginger, garlic, curry powder and garam masala in a separate large bowl. Add 2 tablespoons of the spice butter to the shrimp; add the paprika, season with salt and toss. Add the rice, 1 teaspoon salt and 1/2 cup herbs to the remaining spice butter; toss.
Add the shrimp to the baking sheet with the shallots and spread in a single layer. Top with the rice mixture in an even layer and drizzle with 1/4 cup water. Cover the pan tightly with foil and bake until the rice is hot and the shrimp are cooked through, 16 to 18 minutes.
Stir the shrimp and rice together with a fork. Season with salt and stir in the remaining 1/2 cup herbs. Top each serving with yogurt and cashews.