Preheat the oven to 180°C/Gas mark 4.
Peel and thinly slice three or four of the blood oranges into rounds, removing any pips. Juice the remaining blood orange to yield 3 tablespoons juice.
Pour the juice into a 30 cm (12 inch) ovenproof frying pan and add the butter, cardamom seeds and sugar. Warm gently over low heat, stirring to dissolve the sugar, then arrange the orange slices on top of the caramel. Turn off the heat.
To make the sour cream pastry, combine the flour and salt in a food processor, then add the butter and pulse until the mixture resembles sand. Add the sour cream and pulse until the mixture forms a dough ball.
Wrap in plastic wrap and set aside in the fridge for at least 30 minutes.
Roll the pastry out on a lightly floured workbench to a circle large enough to cover the dish. Gently place the pastry over the orange slices, tucking the edges down inside the dish. Prick the pastry all over with a fork and brush with milk or beaten egg.
Bake in the oven for 30 minutes or until the pastry is golden brown and the caramel is bubbling at the edge. Remove from the oven and let sit for 5–10 minutes. Invert the tarte tatin onto a serving dish and serve with ice cream, cream or custard.