Prep the pan: Preheat oven to 350°F (175°C). Grease and line a 9x5-inch loaf pan with parchment paper.
Mix the dry ingredients: In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
Make the batter: In a large bowl, cream butter and brown sugar until light and fluffy (2–3 minutes). Beat in eggs, one at a time, then vanilla. Mix in the brewed coffee and milk until smooth. Fold in the dry ingredients until just combined, then gently fold in walnuts.
Bake: Pour batter into the prepared pan, smooth the top, and bake for 40-45 minutes, or until a toothpick inserted in the center comes out clean. Let cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Make the buttercream: Beat softened butter until creamy. Add powdered sugar, coffee mixture, vanilla, and salt. Beat until fluffy, adding milk or cream as needed for a spreadable texture.
Frost & serve: Once the loaf is completely cool, spread buttercream generously over the top. Slice and enjoy!