Preheat the oven to 340°F (170°C), conventional/static heat. Line a baking sheet with parchment paper.
To make the oat cookie base, combine the rolled oats, flour, baking powder, salt, both sugars, egg, and softened butter in the bowl of a stand mixer fitted with the paddle attachment. Mix on low speed until a sticky dough forms, or use a large bowl and mix by hand with a spatula. Transfer the dough to the prepared baking sheet and press it into a flat, even layer using damp hands or a spatula. Bake for 18 to 22 minutes, until lightly golden. Remove and let cool completely at room temperature.
Once cooled, break the cookie into pieces and pulse into crumbs using a food processor, or crush by hand in a mixing bowl. Add the melted butter and mix until the crumbs are evenly moistened.
Grease the springform pan with butter. Press the cookie crumbs into the bottom and up the sides of the pan, using the bottom of a measuring cup or spoon to press firmly. Chill the crust while you make the filling.
Whisk together the granulated sugar, brown sugar, and melted butter in a bowl until smooth. Add the egg yolks one at a time, whisking well after each addition. Add the heavy cream and salt, and whisk until the mixture is creamy and completely smooth.
Pour the filling carefully into the prepared crust. Pour slowly and close to the surface so the crust doesn’t break.
Bake for 30 minutes. If bubbles appear, that’s normal. Reduce the oven temperature to 320°F (160°C) and bake for another 10 minutes. The edges should be set, the center slightly jiggly, and the top golden brown.
Let the pie cool to room temperature, then refrigerate overnight.
Dust the top with powdered sugar, slice thinly, and serve chilled with a spoonful of crème fraîche or sour cream.