Build a wood fire in a fire ring (see "Learn to Cook Over Live Fire," below) and let it burn down to low flames and embers (1 to 1 1/2 hours).
Cut foil into twelve 1-ft. squares. Divide into 6 stacks of 2 sheets each and set an apple half on each, cored side up. In a bowl, mix flour, butter, oats, brown sugar, and cardamom with your fingers until evenly moistened with no chunks of butter. Mound an equal amount of topping in each apple cavity.
For each packet, neatly fold one stacked set of corners over an apple half, followed by the opposite set of corners; roll remaining corners snug to fruit to seal.
Using long grilling tongs, move logs from center of fire into a frame to create a flat bed of embers in the center big enough for packets. Remove any flaming wood chunks from ember bed. Set packets, topping side up, on embers. Cook 15 minutes, turning packets over every 5 minutes with grilling tongs and moving positions in ember bed for even cooking. Transfer a packet to a plate and carefully open to check for scorching; if you see any, adjust fire or positions of packets. Cook packets topping side down without turning until topping is lightly browned, 10 to 15 more minutes.
Open packets and let cool a few minutes. In a bowl, whisk whipping cream, crème fraîche, and granulated sugar until thick. Serve with apples.