In a saucepan, combine fresh raspberries, sugar, lemon juice, and cornstarch. Cook over medium heat for 5-7 minutes, stirring frequently, until thickened. Remove from heat and let cool.

In a large bowl, whisk together melted butter and oil. Add sugar, eggs, and vanilla, mixing until smooth.

Sift together flour, cocoa powder, baking soda, baking powder, and salt in another bowl. Gradually add to the wet mixture, alternating with buttermilk until just combined.

Beat cream cheese with sugar until smooth. Add egg yolk and sour cream, mixing until creamy.

Preheat oven to 350°F (175°C) and line a muffin tin. Fill each liner with chocolate batter halfway, add cheesecake filling, and top with raspberry sauce.

Bake for 18-22 minutes, until edges are set. Allow to cool for 10 minutes.

Transfer to a wire rack to cool completely. Refrigerate for at least 30 minutes before serving.

Before serving, drizzle with melted white chocolate and top with whipped cream and a raspberry.