Preheat the oven to 350°F (175°C). Grease a 9" x 5" loaf pan, line with parchment paper, and lightly grease the paper.
Whisk together the flour, baking powder, and salt. Set aside.
Using an electric mixer on medium speed, beat the butter, sugar, and brown sugar until light and fluffy. Add the eggs, one at a time, mixing well after each addition. Mix in the vanilla extract.
Reduce the mixer speed to low. Add the flour in three portions, alternating with two portions of milk. Mix just until combined or a few streaks of flour remain. Set aside 1/4 cup of the chocolate chips, and stir the remainder into the batter.
Transfer the batter to the prepared pan, and spread it evenly. Sprinkle the reserved chocolate chips over the top of the cake. If you like, sprinkle a few pinches of coarse sugar over the top of the batter.
Bake 60 to 65 minutes, or until the top is lightly browned and a pick inserted into the center comes out clean.
Cool in the pan on a wire rack for 10 to 15 minutes. Then remove the cake from the pan and place directly on a wire rack to continue cooling.
Notes
Store in an airtight container at room temperature up to 3 days.