Preheat oven to 350°F (177°C). Line a 9-inch square baking pan (I love this one) with parchment paper, leaving an overhang on the sides to easily lift the bars out of the pan. Set aside.

Using a handheld mixer or stand mixer fitted with a paddle attachment, beat the cream cheese and butter together on medium-high speed in a large bowl until the mixture is smooth and creamy, about 2 minutes. Add the flour, granulated sugar, egg, and coconut extract and beat until fully combined. Finally, beat in the shredded coconut on low speed until combined. Set aside at room temperature.

Slice the butter into Tablespoon-size pieces and melt in the microwave in a large heatproof bowl or in a small saucepan on the stove. (Transfer melted butter to a large bowl if using the stove.) Whisk the oil and granulated sugar into the melted butter. Let it sit for 3-5 minutes to slightly cool. Whisk in the eggs and vanilla extract until combined. Add the cocoa powder, flour, and salt and whisk until combined. Batter will be thick. Fold in the chocolate chips.

(This step does NOT have to be exact or perfect. Do not overthink it– just spoon and swirl.) Spoon about 1/3 of the brownie batter into the prepared pan. Spread it all over the bottom as best you can. Take about 1/3 of the cheesecake batter and drop spoonfuls of it on top of the brownie batter. Use your spoon or a knife to gently swirl together. Use another 1/3 of the brownie batter and drop spoonfuls of it on top. Use another 1/3 of the cheesecake batter and drop spoonfuls of it on top. Gently swirl together. Repeat spooning remaining brownie and cheesecake batters. Gently swirl together.

Bake for 40-42 minutes or until a toothpick inserted in the center comes out with only a few moist crumbs. I recommend tenting the brownies with aluminum foil after about 25 minutes to protect the top from over-browning. Remove from the oven and place the pan on a wire rack. Cool brownies completely.

Lift the brownies out using the parchment paper overhang on the sides. 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.