Preheat the oven: Preheat the oven to 350°F (175°C). Grease and flour a Bundt pan to prevent sticking.
Mix the dry ingredients: In a medium bowl, whisk together the flour, brown sugar, baking powder, baking soda, and salt. Set aside.
Beat the butter and eggs: In a large bowl, beat the softened butter with an electric mixer until light and fluffy, about 2–3 minutes. Add the eggs one at a time, mixing well after each addition. Mix in the vanilla extract and lemon zest.
Combine the wet and dry ingredients: Gradually add the dry ingredients to the butter mixture, alternating with the Greek yogurt. Begin and end with the flour mixture. Mix just until combined. Gently fold in the blueberries.
Fill the Bundt pan: Pour the batter into the prepared Bundt pan and smooth the top with a spatula.
Bake: Bake for 50–60 minutes, or until a toothpick inserted into the cake comes out clean.
Cool: Allow the cake to cool in the pan for about 10–15 minutes before inverting it onto a wire rack to cool completely.
Prepare the glaze: In a small bowl, mix the powdered sugar with 2–3 tablespoons of water until smooth. Adjust the consistency as needed. It should be thick enough to drizzle but fluid enough to pour.
Glaze the cake: Once the cake is completely cooled, drizzle the glaze over the top. Garnish with extra lemon zest if desired.