Line an 8x8-inch baking dish with parchment paper and lightly spray with nonstick spray. Set it aside.
In a small heat-safe bowl, add the all-purpose flour. Microwave for 1 minute, set it aside, and allow the flour to cool completely. Once the flour is completely cooled, sift the flour to remove any small clumps.
Add 1 cup of semi-sweet chocolate chips to a Ziploc bag. Place the chocolate chips in the freezer while making the rest of the recipe.
Using a medium-sized mixing bowl and a handheld mixer, cream the butter, granulated sugar, light brown sugar, milk, vanilla extract, and salt for 1½-2 minutes.
Reduce the mixer speed to low, add in the flour and mix just until the ingredients are well incorporated. Set it aside.
In a heat-safe medium-sized bowl, heat the white chocolate chips and sweetened condensed milk in the microwave for 30 seconds at a time, stirring well after each 30 seconds, until the chips are completely melted and smooth.
Remove the Ziploc bag containing the 1 cup of chocolate chips from the freezer. Using a wooden spoon, stir the frozen chips into the butter and flour mixture.
Spoon the white chocolate mixture into the cookie dough. Stir just until all ingredients are combined.
Spoon the cookie dough fudge into the prepared baking dish.
Evenly sprinkle the remaining 1 cup of chocolate chips on top of the cookie dough fudge. Very gently press the chips into the top of the fudge. Cover tightly and refrigerate for at least 2 hours to overnight.
Remove the fudge from the refrigerator and cut into squares, 5 pieces across and 5 pieces down.
To Store: Store any leftovers in an airtight container in the refrigerator for up to 7 days.
To Freeze: For longer storage, tightly wrap the fudge with plastic wrap and then place it in an airtight container or freezer-safe plastic bag for up to 3 months.
The parchment paper allows you to easily remove this perfect fudge from the square pan to slice.
Since this is an edible cookie dough recipe, the raw flour needs to be microwaved to make certain to kill any pathogens. After the flour completely cools, the flour may need to be sifted because sometimes when either heating the flour in the microwave or the oven, small clumps form due to the moisture.
Freezing the chocolate chips before adding them to the cookie dough mixture and then the melted white chocolate mixture keeps the chocolate from melting and coloring the fudge a streaky brown.
To make it easier to cut later, you can lightly score the top of the fudge with a sharp knife before chilling.