Warm the heavy cream until warm but not boiling. Sift the Dutch-process cocoa powder and cut the room-temperature butter into cubes. Have everything measured and ready before beginning.
Place a medium, heavy-bottomed stainless steel saucepan or sauté pan over low-medium heat. Add the granulated sugar in an even layer. As the sugar begins to melt, stir gently with a heat-resistant silicone spatula, or wooden spoon. The sugar will clump before gradually melting. Continue until completely melted and a rich amber color.
Remove the pan from the heat. Carefully add the cubed butter, a few pieces at a time, stirring continuously. The mixture will bubble vigorously. Continue stirring until the butter is melted and incorporated. If needed, return the pan to low heat briefly to help the mixture come together.
Slowly pour in the warmed heavy cream while stirring continuously. The caramel will bubble aggressively and may temporarily firm up. Return the pan to low heat if necessary, stirring until the mixture is smooth.
Gradually whisk in the sifted Dutch-process cocoa powder. Continue stirring over low heat for approximately 1–2 minutes, or until the cocoa is fully incorporated and the sauce is smooth and glossy.
Remove from the heat and stir in the vanilla bean paste, or extract, and flaky sea salt until combined.
Allow the sauce to cool until no longer hot, then transfer to a clean, heat-safe airtight container. Refrigerate promptly. The sauce will thicken as it cools.
Enjoy chilled for a thicker consistency or warm gently until smooth and pourable before drizzling over your favorite desserts.