Melt the butter in a 2-quart saucier or saucepan over medium-high heat. Add the brown sugar and cook, stirring occasionally, until the sugar has dissolved and the butter smells nutty, 1 to 2 minutes.
Pour in the whole milk, heavy cream, and kosher salt, and bring to a simmer. Then, remove from the heat and cool slightly.
Meanwhile, whisk the sugar and egg yolks together in a large bowl until the mixture is smooth and thick. Add the cornstarch and whisk until smooth.
Temper the warm dairy mixture into the egg mixture by slowly ladling about half a cup of the warm dairy mixture into the egg mixture, whisking constantly. Repeat this process until about a third of the dairy mixture has been added to the eggs. At this point, you can add the remaining dairy all at once.
Strain the pudding base back into the saucepan and return to medium heat. Continue cooking, stirring occasionally until the mixture begins to bubble and thicken. Remove from the heat and add the Scotch and vanilla extract.
Pour the thickened pudding into 6 small ramekins, place a piece of plastic wrap on each and refrigerate until cold and thoroughly set, at least 4 hours but preferably overnight. Sprinkle with flaky salt before serving.