Preheat oven to 400°. In a 12-in. ovenproof frying pan or a 9- by 13-in. baking dish, combine 1 1/2 cups sugar (1 cup if using blueberries), tapioca, cinnamon, and cardamom. Gently mix in lemon juice and berries. Let stand, stirring occasionally, for tapioca to soften slightly, 15 minutes (50 minutes for frozen berries; they'll start to look wet). Spread berries level.
On a floured surface with a floured rolling pin, roll out pastry to a 14-in. round or 10- by 14-in. rectangle, lifting up pastry and re-flouring underneath if needed to prevent sticking. Trim uneven edges with a knife. Slide a rimless baking sheet under pastry and ease it over berries. Fold edges of pastry under so they're flush with pan or dish, pressing together any cracks. Flute pastry edges with a finger and thumb to seal.
Brush crust (but not fluted edges) with milk and sprinkle with remaining 2 tbsp. sugar. Cut about 6 vents in crust to release steam. Bake until crust is golden brown and filling is bubbling through vents, 50 to 60 minutes; tent with foil if pastry starts to get too brown, and put a rimmed baking sheet underneath if the cobbler starts to bubble over.
Supporting cobbler underneath, carefully transfer to a rack and let cool at least 45 minutes. Serve warm or cool, with crème fraîche to spoon on top.
*Buy huckleberries from specialty produce markets or pick your own, from your garden if you grow them or from the wild. Huckleberries range from blue-purple to red and even white; they thrive in subalpine forests and meadows in many Western states. In the Cascades, respect posted areas reserved for the Yakama Indian Nation.
Note: Nutritional analysis is per serving.