Preheat the oven: Preheat your oven to 350°F (175°C). Grease and flour a bundt pan thoroughly to ensure easy release.
Prepare the dry ingredients: In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
Cream butter and sugar: In a large bowl, beat the softened butter and granulated sugar until light and fluffy, about 3-5 minutes.
Add eggs and vanilla: Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in the vanilla extract.
Combine wet and dry ingredients: Gradually add the dry ingredients to the butter mixture, alternating with sour cream and milk. Begin and end with the dry ingredients, mixing until just combined.
Fold in the blueberries: Gently fold in the blueberries to keep them whole and evenly distributed throughout the batter.
Optional swirl: If using blueberry jam, spoon dollops over the batter and gently swirl with a knife.
Bake: Pour the batter into the prepared bundt pan and smooth the top. Bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean.
Cool the cake: Let the cake cool in the pan for 15 minutes, then transfer it to a wire rack to cool completely.
Make the glaze: In a small bowl, whisk together powdered sugar, blueberry puree, and vanilla extract until smooth. Drizzle over the cooled cake before serving.