Preheat your oven to 350°F (175°C) and lightly grease a doughnut pan with cooking spray.
In a large mixing bowl, whisk together the flour, brown sugar, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt until thoroughly combined.
In another bowl, mix the buttermilk, applesauce, egg, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir gently until just combined; be careful not to overmix.
Transfer the batter to a piping bag (or a plastic bag with one corner cut off) for easier filling.
Fill each doughnut cavity about halfway with batter, then add a small dollop of speculoos spread in the center of each. Top with more batter, filling the cavities about 3/4 full.
Bake in the preheated oven for 12-15 minutes or until a toothpick inserted into the doughnuts comes out clean.
Allow the doughnuts to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
Once cooled, dust with powdered sugar before serving.