To make the cookies: Preheat oven to 350 degrees F. Line a baking sheet with parchment. In the bowl of a stand-up mixer, with the paddle attachment, add the butter, olive oil and sugar. Beat until light and fluffy, about 2 minutes.
Next, add the baking powder, salt and egg. Beat once more until combined. With the mixer on low and alternating between the flour and milk, add them both to the mixture, until no flour speckles are visible. Transfer to a piping bag (no tip needed!) or you can also use a Ziplock freezer bag. Pipe rounds of batter onto the baking sheet, spacing them about 3 inches apart.
Transfer to the oven to bake for 7 to 9 minutes, until they spring back when touched. Repeat with the remaining batter. Allow to cool completely before frosting.
To make the frosting: To a small saucepan, set over medium heat, add the blackberries, salt, lemon juice and sugar. Cook for 4 to 5 minutes, until softened. Smash them with a spoon and run through a sieve, discarding the pulp. Transfer the blackberry puree to the fridge to cool (or else it’ll melt the frosting!).
To a medium bowl, add the unsalted butter, powdered sugar and the cooled blackberry sauce. Beat until combined.
To decorate the cookies: Add a teaspoon of frosting to each cookie. Make a pretty smear situation and top with a sprinkling of dried rose petals and pistachios. Or if you don’t have dried rose petals, use sprinkles!