Place sweet potatoes in a large saucepan and cover with water. Bring to a boil. Reduce heat to a simmer and cook until tender, 10 to 15 minutes. Drain well and transfer to a food processor. Process until smooth.
Preheat oven to 350 degrees F. Coat an 8-inch-square (or similar 2-quart) broiler-safe baking dish (see Tip) with cooking spray.
Whisk whole eggs, brown sugar, cinnamon, oil, evaporated milk, vanilla and salt in a large bowl until smooth. Add the sweet potato; whisk until smooth. Stir in pineapple and its juice. Spread the mixture in the prepared baking dish. Sprinkle with pecans.
Bake the casserole until heated through and the edges are bubbling, 35 to 45 minutes. Set aside while you make the topping.
To prepare meringue topping: Position rack in top third of oven; preheat broiler. Beat egg whites in a medium bowl with an electric mixer at high speed until soft peaks form (see Tip). Beat in granulated sugar in a slow, steady stream. Continue beating until stiff peaks form.
Spoon the meringue into a gallon-size sealable bag. Seal the bag, pressing out as much air as possible. Cut a 1/2-inch hole in one corner. Pipe the meringue onto the casserole, making marshmallow-size dots. (Alternatively, use a pastry bag fitted with a 1/2-inch tip or spread the meringue over the casserole as if you were frosting a cake.) Broil until lightly browned, watching carefully to prevent burning, 30 to 90 seconds.