Preheat oven to 450°F with racks in upper third and lower third positions.
Stir together brown sugar, salt, 1 tablespoon curry paste, and 1 tablespoon oil in a small bowl.
Brush cut sides of each squash half with oil mixture.
Place squash, cut sides down, on a large rimmed baking sheet greased with oil.
Stir together rice, coconut, 2 tablespoons oil, and remaining ¼ cup curry paste in a large bowl.
Drizzle remaining 1 tablespoon oil on a second large rimmed baking sheet.
Spread rice mixture in an even layer on second baking sheet.
Place pan with rice on the top oven rack and pan with squash on bottom rack.
Roast rice until golden and crisp on the bottom, 25 to 30 minutes; roast squash until tender, 30 to 40 minutes.
Flip squash cut sides up; let stand until slightly cooled, about 10 minutes.
Scoop flesh from neck portion of each squash half, leaving a ½-inch border; place scooped flesh in a large bowl.
Add cashews, cilantro, scallions, mint, fish sauce, lime zest and juice, and crispy rice to bowl; stir gently to mix.
Divide mixture evenly, and stuff into cavities of the 4 squash halves.
Garnish with cashews, scallions, and mint, and serve with lime wedges.
