Preheat the oven to 350°F / 175°C. Butter and generously coat a 12 cup capacity bundt pan with sugar.
In a medium sized bowl, whisk together the flour, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or with a hand mixer), beat together the butter, oil, and sugar for 5 minutes until light and fluffy.
Scrape down the sides of the bowl, and add in one whole egg at a time, beating for 20 seconds between each addition until well combined. Add in both egg whites and the vanilla and beat until well combined.
Alternate between adding the flour mixture and the sour cream and milk. Fold in 1/3 of the flour mixture, then 1/2 of the sour cream and milk, Fold in half of the remaining flour mixture, all of the remaining sour cream and milk, and then the remaining flour mixture.
Remove half of the batter and place it into a medium sized mixing bowl. In a small bowl, mix together the butterfly pea powder and 2 tbsp. milk.
To ½ of the batter, gently fold in the butterfly pea powder mixture just until combined.
Evenly spread ~⅓ of the vanilla batter into the bundt. Use ~⅓ of the blue batter to place big dollops over the vanilla, then carefully spread it over the vanilla. Repeat for a total of 6 layers.
Use a knife to gently swirl the batters together.
Bake for 50-60 minutes, until a knife inserted in the bundt comes out clean or with only a few moist crumbs.
Let the cake cool in the pan for 15-20 minutes. Then, place a wire rack on top of the bundt pan and flip it over to get the cake out. Allow the cake to fully cool to room temperature before putting on the icing.