Preheat your oven to 350°F (175°C) and grease your baking dish or cake pan.
In a mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Add the eggs, one at a time, beating well after each addition. Stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the butter mixture, alternating with the sour cream. Mix until just combined.
Fold in the cooled brewed coffee, ensuring it is evenly incorporated into the batter.
Pour the batter into the prepared baking dish or cake pan, spreading it out evenly.
Bake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Remove from the oven and allow the coffee cake to cool for a few minutes in the pan before transferring it to a wire rack to cool completely.