Step 1

Preheat oven to 350º F (180º C). Line a square baking pan (8 x 8 inches | 20 x 20 cm) with parchment paper and lightly spray with baking spray. Set aside.

Step 2

Place butter, sugar, and oil in a large microwave-safe bowl. Microwave for 30 seconds, then remove and stir with a whisk. Repeat process 2-3 more times until the mixture looks glossy and the butter is completely melted.

Step 3

Add yogurt and vanilla extract; mix until well incorporated.

Step 4

Add in flour, cocoa powder, baking powder, baking soda, and salt; continue to mix until just combined. Please DO NOT overmix the batter.

Step 5

Reserve 1/4 cup of the brownie batter in a separate bowl. Set aside.

Step 6

Spread the batter in the prepared baking pan. Set aside.

Step 7

Mix cornstarch and water in a small bowl until smooth. Set aside.

Step 8

Place the cream cheese in the bowl of an electric mixer, beat on low speed for 2-3 minutes until smooth and free of any lumps. Add sugar and sour cream and continue mixing until incorporated. Gradually add sweetened condensed milk and beat, scraping down the bowl as necessary, until creamy, for 2 minutes.

Step 9

Add lemon juice, vanilla extract, heavy cream, and cornstarch mixture; beat on high speed until well incorporated, about 2 minutes.

Step 10

Pour cheesecake over prepared brownie batter.

Step 11

Take your reserved 1/4 cup brownie and dollop the batter over the cheesecake batter. NOTE: if it has become too stiff, just stir in 1 teaspoon of milk and mix it with a spoon. Use a skewer or knife to swirl the two batters together.

Step 12

Bake for 35 – 40 minutes or until, or until the brownies begin to pull away from the edges of the pan. IMPORTANT: Unlike other recipes, these will not have a springy center, and a skewer inserted into the center will NOT come out clean. Your brownies are done when the center looks set, with a little wiggle, and you see the edges puff up, and it just begins to brown and crack.

Step 13

Allow the brownies to cool in the pan set on a wire rack for 1-2 hours. Then cover and refrigerate for at least 2 hours and up to 1 day. Allow to cool COMPLETELY before cutting and serving; the cheesecake layer must be cold before cutting into squares.

Step 14

Use the parchment overhang to lift the brownies out of the pan. Cut into squares, then serve. NOTE: For neat squares, I use a very sharp knife and wipe it clean with a paper towel after each cut.