Place 1 cup of pistachios in a food processor and process for about 5 minutes, scraping down the sides every minute, until it forms a sand-like consistency. Add the 3 teaspoons olive oil and then process again for 3 more minutes, or until it achieves a nut-butter consistency.
In a large bowl, add the softened butter, sugar, and 3 tablespoons of the pistachio butter. Beat with an electric mixer until fluffy. Then mix in the eggs, vanilla, and milk
In a large bowl, whisk together the flour, baking powder, baking soda, and 1/4 teaspoon salt. Add half of the flour mixture to the wet, beat until incorporated, then add in the rest of the flour mixture and mix until evenly combined.
Grease a 9x13" pan with 1 teaspoon of spray oil and pour the batter in. Spread out as best you can (some gluten-free flours can be gummy at this stage and hard to spread - just keep working with it, the results will be great). Bake at 350F for 15-20 minutes, or until a toothpick comes out clean the top is lightly golden.
Let the cake cool completely before making the frosting.
For the frosting, add the cottage cheese to the food processor with the remaining pistachio butter and blend until smooth, about 3 minutes. Pour into a bowl and add the powdered sugar and 1/4 teaspoon salt. Beat with a mixer until smooth.
Once the cake is cooled, pour the frosting over the cake and spread out into an even layer. Roughly chop the remaining 1/4 cup of shelled pistachios and sprinkle over the top. Cut into pieces and enjoy!
Notes
If you're using store-bought pistachio butter (vs. making your own like I have here), you'll need about 6 ounces total for this recipe.