Fill a large bowl with cold water. Add chard to bowl, and agitate leaves to remove dirt. Drain chard; repeat washing process twice. Set aside.
Bring 2 quarts water to a boil in an 8-quart pot over high. Add chard and 3 tablespoons salt, and stir until chard is wilted enough to be fully submerged. Cook, stirring occasionally, until tender, 8 to 10 minutes. Drain chard, and set aside until cool, about 20 minutes.
Working over a sink, squeeze cooled chard to release as much water as possible. Finely chop chard into small pieces (no bigger than ¼ inch).
Preheat oven to 350°F. Place raisins in a small bowl, and cover with ⅓ cup warm water. Set aside to let raisins soak. Heat ⅓ cup oil in a large skillet over medium. Add onion; cook, stirring often, until softened and starting to brown slightly, about 7 minutes. Add chopped chard; increase heat to high. Cook, stirring often, until chard darkens slightly and starts to stick to bottom of skillet, about 8 minutes. Transfer mixture to a medium bowl; let cool to room temperature, about 20 minutes.
Meanwhile, place breadcrumbs in a medium skillet, and cook over medium-low, stirring often, until lightly toasted, 2 to 3 minutes. Transfer to a small bowl; set aside.
Add cheese, eggs, and pine nuts to cooled chard; stir to combine. Drain raisins, and squeeze to release any excess liquid; add to chard mixture. Stir in pepper and remaining ¾ teaspoon salt.
Brush bottom and sides of a 9-inch springform pan with 1 tablespoon oil. Add half of breadcrumbs to pan, spreading to evenly cover bottom and sides of pan. Add chard mixture, pressing gently to smooth top without compacting the chard. Sprinkle with remaining half of breadcrumbs; drizzle with remaining 1 tablespoon oil.
Bake torte in preheated oven until golden brown, 35 to 40 minutes. Remove from oven; let cool slightly, about 5 minutes. Run a knife around edge of torte to loosen, and remove pan sides. Let cool 5 to 6 minutes. Slide a spatula under torte to release it from bottom of pan; slide torte, without inverting, onto a platter. Serve warm or at room temperature.
