Step 1Heat the oven to 325 degrees. Line a rimmed baking sheet with foil.
Step 2Place the salmon fillets on the prepared baking sheet and season all over with salt and pepper. In a small bowl, whisk together the yogurt, olive oil and curry paste until smooth, then spoon evenly over the fillets, spreading each to completely cover the tops of the salmon. Bake until an instant-read thermometer inserted in the thickest part of each fillet reads 160 degrees, about 35 minutes for 1- to 1 ½-inch-thick fillets.
Step 3While the salmon bakes, heat a small skillet over medium-high heat. Add the cashews and cook, tossing occasionally, until toasted and warm, about 2 minutes. Transfer to cutting board and roughly chop.
Step 4Place the cucumber slices in a medium bowl, sprinkle with salt and pepper and let stand, massaging occasionally with your fingers, until soft, at least 30 minutes.
Step 5Remove the salmon from the oven and transfer each fillet to a plate. Scatter the cashews over the top of each fillet and serve with cucumbers on the side.
Red Peanut: Swap one-fourth cup Thai red curry paste for the green curry paste and swap peanuts for the cashews.
Beet and Dill: Swap 1 1/3 cups mayonnaise for the yogurt, omit the green curry paste and season each fillet with 1 tablespoon soy sauce instead of salt and pepper. Omit the cashews and sprinkle the cooked fillets with half a cup roughly chopped dill fronds. Swap 1 pound cooked small red or yellow beets for the cucumbers.
Green Goddess: Swap ½ cup finely chopped mixed soft herbs, such as flat-leaf parsley, dill, tarragon and basil, for the green curry paste.