Preheat the oven to 375F/190C. Lightly butter a 10 - 11 inch (25 - 28cm) diameter round shallow baking dish.
Place the ingredients for the base (butter, egg, sugar, flour, oats, baking powder, salt and cardamom) in a food processor and pulse together to mix them well. The mixture will come together as a fairly soft dough. If you don't have a food processor, you can beat the butter and sugar, then add in the egg followed by the dry ingredients.
Press the base mixture into the baking dish, pressing all the way to the edges and up the sides slightly to give a slight rim (if your dish is shallow, around 1in/3cm deep) you can press right up to the top edge, but lower if the dish is deeper). Smooth the bottom of the dough relatively flat.
Place the dish with the dough in the fridge to chill gently while you prepare the filling. Wash the blueberries and pick over ot remove any stems.
Combine the sour cream, sugar, egg and vanilla extract, if using, and whisk together to be smooth and well combined.
Place the blueberries over the base mixture in the baking dish and spread in an even layer. If you like, you can keep some back to place on top of the cream layer, or instead do as I did here and lift a few up after adding and cream and clean off the top edge so they show through a little.
Pour the sour cream mixture over the blueberries and spread evenly. If you like, you can keep all the blueberries under the cream layer or, as mentioned above, you can lift a few up and clean off the top to let a little of the berry show through. Alternatively, if you reserved a few blueberries, dot them evenly so they are partly under cream, partly above.
Place the dish on a baking sheet to catch any drips, then bake the pie for approximately 30 - 40 minutes until the edges are crisp and the top is dry and seems gently set (it will firm a little more as it cools). If the cream is gently brown at the edges, that's fine, but you want to avoid the base layer edges being too brown.
Allow the pie to cool a good 30 minutes or more before serving.