Preheat your oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan or line it with parchment paper for easy removal.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy using an electric mixer.
Add the eggs, one at a time, mixing well after each addition. Then, mix in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, cinnamon, and salt. Gradually add the dry ingredients to the wet mixture, alternating with the milk. Mix until just combined.
In a small bowl, combine the brown sugar, ground cinnamon, and chopped nuts (if using) for the swirl filling.
Pour half of the batter into the prepared baking pan and spread it evenly. Sprinkle half of the cinnamon-sugar mixture over the batter.
Pour the remaining batter over the swirl filling, smoothing it out, then sprinkle the rest of the cinnamon-sugar mixture on top.
Using a knife or skewer, gently swirl through the batter to create a marbled effect, being careful not to overmix.
Bake in the preheated oven for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Let the coffee cake cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
Notes
Serve slices warm or at room temperature, dusted with powdered sugar and accompanied by coffee.