1. 1. Preheat oven to 350°F (175°C). Line a 9×9-inch metal baking pan with parchment paper, leaving overhangs for easy removal. Lightly grease the parchment.

2. 2. Melt butter and 1 cup chocolate chips in a large microwave-safe bowl. Heat in 20-second bursts at 50% power, stirring between each until smooth, about 2 minutes. Whisk in cocoa powder until fully incorporated.

3. 3. Stir in granulated sugar, brown sugar, eggs, egg yolk, vanilla, and coffee powder. Whisk vigorously for 2 minutes until glossy and thick. Scrape bowl sides.

4. 4. Sift flour and salt over the batter. Fold gently until just combined, avoiding overmixing for fudgy texture. Fold in remaining 1/2 cup chocolate chips.

5. 5. Reserve 1/3 cup brownie batter in a small bowl. Spread remaining batter evenly into prepared pan. Refrigerate while making cheesecake layer.

6. 6. Beat softened cream cheese on medium speed for 2 minutes until creamy and lump-free. Add sugar and salt, beat 1 minute. Add eggs one at a time, then vanilla, mixing on low until smooth. Scrape bowl.

7. 7. Pour cheesecake batter over chilled brownie base, smoothing with an offset spatula.

8. 8. Thin reserved brownie batter with 1-2 tbsp hot water until pourable like cake batter. Dollop spoonfuls over cheesecake. Swirl gently with a skewer or toothpick for marbled effect, wiping edges clean.

9. 9. Bake at 350°F for 20 minutes (par-bake brownie base). Reduce to 325°F and bake 25-35 minutes more. Edges puff and crack slightly; center sets with slight jiggle.

10. 10. Cool in pan on wire rack 30 minutes. Refrigerate 2+ hours or overnight for clean slices. Lift out using parchment, cut with hot knife.