Line your 9x9 inch baking pan with parchment paper, leaving overhang on the sides for easy removal.
In a saucepan over low heat, melt the butter gently until it starts to shimmer and smells toasted—about 2 minutes.
Add the sugar and cocoa powder to the melted butter, stirring constantly until the mixture becomes glossy and smooth, about 3 minutes; it should smell rich and chocolatey.
Pour in the heavy cream and stir until the mixture bubbles and thickens, about 2 minutes; it will look glossy and slightly viscous.
Remove the pan from heat and stir in vanilla extract. Then add the chocolate chips, waiting for them to melt into the mixture, stirring until smooth and shiny.
Pour the thick, glossy fudge mixture into your prepared pan, spreading it evenly with a spatula and gently tapping the pan to settle the surface and remove air bubbles.
Bake in a preheated oven at 180°C (350°F) for 20-25 minutes. The edges should crack and pull away from the sides, with a shiny, crackled top.
Remove the pan from the oven and let it cool in the pan for 15 minutes; the surface should be set and crackled.
Lift the fudge out using the parchment overhang and transfer it to a wire rack to cool completely, about an hour, until firm.
Once cooled, refrigerate for 30 minutes to firm up for cleaner slicing.
Use a sharp knife warmed slightly in hot water to cut neat squares, then serve at room temperature or chilled for a gooey or firm texture.