In a medium saucepan, melt butter. Whisk in brown sugar, and cook over medium heat for 5 minutes, stirring often.
Meanwhile, heat 1/2 cup milk in the microwave for 30 seconds, or until hot but not boiling. Whisk in cornstarch. Pour through fine mesh strainer to eliminate any lumps, then whisk in 2 eggs.
Remove sugar mixture from heat. Pour remaining 3/4 cup of milk, and all the cream, into the brown sugar mixture, whisking well. When completely combined, whisk in cornstarch mixture.
Cook over medium heat, stirring constantly, until pudding comes to a simmer. Cook for one additional minute. If you feel very strongly about eliminating every last lump, you may want to strain one more time - however, pudding is very thick at this point.
Spoon into bowls. Cover tops with plastic wrap, and chill for at least 4 hours. Serve topped with whipped cream.