Preheat your oven to 375°F (190°C). Butter a baking dish generously to prevent sticking and ensure even browning.
In a large mixing bowl, combine sliced peaches with granulated sugar, freshly ground cardamom, and lemon juice. Toss gently to evenly coat the fruit, then pour it into the prepared baking dish.
In another bowl, stir together the rolled oats, flour, brown sugar, and salt. Add the cold butter pieces and use a pastry cutter or fork to cut the butter into the dry ingredients until the mixture resembles coarse crumbs.
Evenly sprinkle the oat topping over the peach filling, covering all the fruit for a uniform crust and topping.
Bake in the preheated oven until the topping is golden brown and bubbling around the edges, about 35 minutes. Check around the 30-minute mark to prevent over-browning.
Remove the dish from the oven and let it cool slightly; the filling will thicken as it cools while the topping remains crisp. Serve warm, preferably with a scoop of vanilla ice cream or a dollop of whipped cream.