Adjust the oven rack to the lower-third position and preheat the oven to 350°F (177°C). Line the bottom and sides of an 11×7-inch baking pan with parchment paper, leaving an overhang on the sides.

Melt butter and semi-sweet chocolate together in a medium saucepan on medium heat, stirring constantly. Remove from heat and let cool to room temperature, about 15 minutes.

Whisk sugar into cooled chocolate/butter mixture. Add in the eggs one at a time, whisking after each addition until combined. Whisk in the vanilla, and then gently fold in the flour and salt. Pour batter into prepared pan, reserving about 1/4 cup of batter.

In a large bowl, beat the cream cheese on medium-high speed until smooth and creamy, about 1 minute. Beat in the sugar, egg yolk, peppermint extract, and 2 drops of food coloring until completely smooth, about 1 minute. Fold in the mini chocolate chips.

Dollop spoonfuls of the cream cheese mixture on top of the prepared brownie batter. Spoon remaining 1/4 cup of brownie batter on top. Glide a knife through the layers, creating a swirl pattern. Add more mini chocolate chips on top, if desired.

Bake brownies for 30–35 minutes, or until a toothpick comes out mostly clean with just a few moist crumbs. Tent the brownies with aluminum foil after about 20 minutes to protect the top from over-browning. Remove from the oven and place the pan on a wire rack to cool completely.

Lift the brownies out using the parchment paper overhang on the sides and cut into squares.

Cover leftover brownies and store at room temperature for up to 1 day or in the refrigerator for up to 1 week.