In a medium heavy saucepan, combine 2 cups of the cream, the milk, sugar, and salt and bring to a gentle boil over medium heat, whisking to dissolve the sugar. Remove from the heat.

In a medium bowl, combine the egg yolks and cornstarch and whisk until pale yellow in color.

Slowly add ½ cup of the hot cream mixture into the egg yolks, whisking constantly until smooth. Gradually add the egg mixture to the remaining hot cream and whisk well to combine. Bring to a simmer, stirring constantly with a heavy wooden spoon and cook until the mixture thickens, 4 to 5 minutes. Remove from the heat and whisk in the butter pieces, 2 teaspoons of the Scotch, and the vanilla extract. Whisk until the butter is melted.

Strain through a fine mesh strainer into a clean bowl. Spoon into 4 individual dessert bowls or decorative glasses and cover each with plastic wrap, pressing down against the surface to prevent a skin from forming. Chill in the refrigerator for at least 4 hours.

In a medium bowl with an electric mixer on medium speed, whip the remaining ½ cup cream until thick and foamy. Add the sugar and remaining teaspoon Scotch and continue whipping until the cream holds soft peaks.

To serve, spoon a dollop of the whipped cream onto each serving and serve with butter cookies on the side.