In a deep heavy saucepan combine the brown sugar, maple syrup, and cream and cook the mixture over moderate heat, stirring and washing down any sugar crystals clinging to the sides of the pan with a brush dipped in cold water, until the sugar is dissolved.
Bring the mixture to a boil and boil it, undisturbed, until a candy thermometer registers 250 degrees F.
Remove the pan from the heat, add the butter, and swirl the pan gently until the butter is melted. Let the maple caramel cool for 5 minutes.
Push a wooden skewer or chopstick through the length of each apple and holding the apples by the skewers dip the apples 1 at a time in the maple caramel, coating them well and letting the excess drip off.
Put the apples on buttered baking sheets until the maple caramel is cool and firm. Serve the apples immediately.