In a large mixing bowl, cream butter and sugar using an electric whisk for about 8 minutes until light and fluffy.
Add vanilla extract, then beat in eggs one at a time, whisking thoroughly after each addition.
In a separate bowl, sift together flour, baking powder, and salt.
Gradually add the dry ingredients to the wet mixture in batches, alternating with the milk, beginning and ending with the flour. Mix just until a thick batter forms.
Gently fold in the chopped mulberries.
Preheat oven to 350°F (175°C). Grease and flour a 9-inch bundt pan.
Pour batter into the prepared pan and smooth the top.
Bake for 40–45 minutes or until a skewer inserted into the center comes out clean.
Let the cake cool in the pan for 10–15 minutes before turning it out onto a wire rack.