Combine butter and brown sugar in a small saucepan. Cook over medium heat, whisking constantly, until mixture begins to bubble. Continue cooking, whisking constantly, for 1 minute. Remove from heat. Slowly whisk in ¼ cup heavy whipping cream until smooth. Cool caramel about 15 minutes. Pour the caramel over the Oreo crust, then return to freezer for about 30-45 minutes until just chilled and set. (You don't want the caramel to fully freeze.)
Place chocolate chips in a glass bowl. In a saucepan, bring 1 cup heavy whipping cream to a simmer over medium-high heat. Pour the cream over the chocolate chips and let sit for 5 minutes, then whisk until completely smooth. Pour the chocolate over the caramel and freeze for a final 30 minutes, until just chilled and set. OR refrigerate, covered, until ready to serve. Before serving, sprinkle the top with a flaky sea salt.