In a large bowl, cream the butter and sugar until smooth. Add the oil, milk, vanilla, baking powder, and egg and mix until combined.
Like many Turkish recipes you’ll find, the amount of flour is very helpfully given as “as much as is needed for the dough.” Start with about 3 1/2 cups of flour (~450-550 g), and bring the mixture together until it forms a dough. The dough should be soft, but stiff enough to be filled and shaped. It’s a very forgiving recipe, and you can add more flour as needed at any point.
Refrigerate the dough for one hour.
Mix the candied orange peel, dried apricot, and crushed walnuts together in a large bowl until even. Add the date paste and “knead” together until well-combined. Divide into four equal pieces.
Preheat the oven to 325F, and line a large baking tray with parchment paper.
Remove the dough from the refrigerator, and turn on to a clean surface. Divide the dough into four equal pieces. Starting with one piece, roll into a “log” about as long as the baking sheet, and flatten until you have a rectangle about two inches wide. Roll one piece of the filling to the same size, and wrap inside the dough. Flatten the roll, then cut into 2-inch pieces. Repeat with the rest of the dough and filling.
Press the cut ends of each kurabiye into a shallow bowl of sesame seeds to coat. Place on the baking sheet, and make an indentation with a fork on the top of the kurabiye.
Bake for 25-30 minutes, or until light gold on top. These will keep for up to two weeks in an airtight container at room temperature.