Preheat oven to 350 degrees. Grease and flour a 9x5 inch loaf pan.
Melt the butter in the microwave in a large mixing bowl, set aside to cool slightly for about 5 minutes.
To the butter add the eggs, sugar, Greek yogurt, lemon juice, lemon zest, and vanilla extract. Mix using a hand mixer for 2-3 minutes until well combined.
In a small bowl whisk together the flour, baking powder, and salt.
Add the dry ingredients to the wet and use a spatula to stir just until combined.
If desired, toss the blueberries with the cornstarch, then mix into the batter. You can also skip this step and stir the blueberries in if you don't have cornstarch.
Bake in preheated oven for 45-60 minutes.
Remove the pan from the oven and allow the cake to sit for 10 minutes before gently removing from the pan to a wire rack. Cool completely before glazing.
FOR THE BLUEBERRY SYRUP:
Add the blueberries, water, and sugar to a small saucepan and bring to a simmer over medium heat.
Stir constantly for 3-4 minutes, breaking up the blueberries with a spoon as you stir until thickened and deep blue in color. Remove from the heat and set aside to use in the glaze.
FOR THE GLAZE:
In a medium mixing bowl combine the powdered sugar, blueberry syrup, and lemon juice. Use a hand mixer (a stand mixer is fine too) and beat on medium speed for 2-3 minutes until smooth. Pour over the cooled cake as desired.
NOTE: The cornstarch can help keep the berries from sinking, but this is an optional step. You can also first add some of your plain batter to your cake pan, then, stir the blueberries into the remaining batter and pour on top. That will also help with the berry sinking issue!