Preheat oven to 325°F and grease a 9-inch springform pan; line the bottom with parchment paper.

In a medium bowl whisk together 1/2 cup cocoa, 3/4 cup sugar, and 1/2 teaspoon salt; stir in 1/2 cup melted butter, 2 eggs, and 1/2 teaspoon vanilla until smooth, then fold in 1/3 cup flour until just combined.

Spread the brownie batter into the prepared pan to form a thin, even layer about 3/4 inch thick and bake for 12 minutes; remove and cool while preparing the cheesecake.

Reduce oven to 300°F. Beat 24 ounces room-temperature cream cheese in a large bowl until smooth, add 3/4 cup sugar and 1 teaspoon vanilla and beat until combined, then add 2 whole eggs plus 1 yolk, 1/2 cup sour cream, 2 teaspoons cornstarch, and 1/4 teaspoon salt and mix until velvety but not airy.

Pour the cheesecake batter over the warm brownie base and smooth the top; scatter 3/4 cup candy-coated chocolate pieces on top, pressing a few lightly into the batter.

Place the springform on a rimmed sheet pan and bake at 300°F for 40–45 minutes, until the center has a slight wobble or reaches 125–130°F.

Turn off the oven, crack the door, and let the cheesecake cool in the oven for 30 minutes; transfer to a wire rack to cool to room temperature about 1 hour.

Cover and refrigerate at least 3 hours (overnight preferred) before slicing; run a warm thin knife around the edge, release the springform, and slice, wiping the knife between cuts for clean pieces.