Preheat the oven to 175°C / 350°F. Lightly grease a glass or ceramic baking dish, about 2.3 litres or 2.4 quarts, with butter.
Prepare the pineapple if using fresh. Slice off the top and bottom, stand the pineapple upright, remove the skin, trim away the eyes, cut the pineapple into quarters, remove the tough core, and cut the fruit into bite-size chunks.
Add the pineapple chunks to a bowl with 3 tablespoons brown sugar and 1 tablespoon cornstarch or cornflour. Toss until the fruit is lightly coated, then spread it evenly in the prepared baking dish.
In another bowl, combine the remaining brown sugar, flour, rolled oats, and cold butter. Stir first, then rub the butter into the dry ingredients until the mixture forms a rough, crumbly topping.
Scatter the crumble evenly over the pineapple without pressing it down firmly.
Bake for 40 to 45 minutes, until the topping is lightly golden and the pineapple juices are bubbling around the edges.
Let the crisp cool for 10 to 15 minutes before serving so the juices settle slightly.
Serve warm with vanilla ice cream, cream, or custard.