Preheat the oven to 350°F. Line a 9-inch square baking pan with parchment paper, leaving an overhang on two opposite sides for easy removal.

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

In a large microwave-safe bowl, melt the butter in 30-second increments. Whisk in the oil and sugar; let cool for 3 to 5 minutes. Whisk in the eggs and vanilla until smooth. Add the cocoa powder, flour, and salt; whisk until a thick batter forms. Fold in the chocolate chips.

Spoon about one-third of the brownie batter into the prepared pan and spread it evenly. Drop about one-third of the cheesecake batter in spoonfuls over the brownie layer; gently swirl with a knife or spoon. Repeat with another third of the brownie batter, another third of the cheesecake batter, and swirl again. Finish with the remaining brownie batter and cheesecake batter, swirling gently one last time.

Bake for 40 to 42 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. After 25 minutes, tent the pan loosely with aluminum foil to prevent over-browning. Remove from the oven and cool completely on a wire rack.

Lift the brownies out of the pan using the parchment overhang. Cut into 16 squares.

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