Preheat oven to 350 F. Grease a 9x9-inch baking pan, and line with parchment paper. Set aside.
Melt butter and chocolate chips in a heavy saucepan over low heat, stirring frequently, until melted. Remove from heat, and set aside.
In a separate bowl, beat cream cheese and 1/2 cup sugar together until smooth.
Mix in 1 egg, 2 tablespoons flour, vanilla extract, and a pinch of salt. Set aside.
In a separate large bowl, mix the remaining 1 cup granulated sugar, brown sugar, and 3 eggs together until smooth and well-combined.
Add vanilla and chocolate mixture, and mix until well-combined.
Stir in remaining 1 cup flour and salt until combined.
Spread 3/4 of brownie mixture into prepared pan.
Pour the cream cheese mixture over brownie layer, and spread evenly.
Top with remaining brownie batter, and gently spread to cover cream cheese mixture.
Bake for 40-50 minutes, or until a wooden toothpick comes out with just fudgy crumbs.
Cool on a wire rack for until the brownies are at room temperature.
Freeze for at least 45 minutes.
Let the brownies sit for 10-15 minutes before cutting and serving.
Notes
Butter: I use salted butter.
Bittersweet chocolate chips: Feel free to use semisweet chocolate chips if you can't find bittersweet (dark) chocolate chips. The brownies will just be a tad sweeter.
Brown sugar: Light or dark brown sugar will work. I use light brown sugar.
All-purpose flour: Be sure to properly measure the flour by either weighing it (find the measurements by clicking on "metric") or by sifting/stirring it to break it up. Lightly spoon into a measuring cup and level.
Cover and store any leftover brownies in the freezer.