Preheat the oven to 325 F, and position a rack in the center of the oven. Lightly spray a 9 inch round cake pan with non-stick baking spray, and line the bottom of the pan with a circle of parchment paper.
In a bowl, combine the sugar, orange zest, lemon zest and dried rose petals. Use your fingers to rub everything into the sugar until fragrant.
In a saucepan, melt the butter over medium heat. Continue to cook the butter until nutty, golden brown milk solids form at the bottom of the pan. This process might take about 10 minutes. First the butter will hiss and splatter as the water evaporates, then as it quiets down, a layer of foam will form on top of the butter. This means the butter is done. Immediately remove from the heat, and scrape the butter, including the brown milk solids, into a large bowl. Let cool for 10 minutes.
To the sugar mixture, add the cooled brown butter, eggs, vanilla extract, almond extract, milk and sour cream, whisking until combined.
In a separate bowl, whisk together the flour, almond flour, chopped pistachios, baking powder, salt and cardamom. Add the dry ingredients to the wet, whisking just until moistened.
Pour the batter into the prepared pan. Bake for about 40-45 minutes, until a toothpick or cake tester comes out clean or with moist crumbs clinging to it.