Wash and completely dry the apples. Insert a stick into the stem end of each.
Line a 9-by-9-inch or 7-by-11-inch baking pan with foil. Place the chopped nuts into the lined pan.
Fit a heavy-bottomed saucepan with a candy thermometer. Over high heat, cook 3/4 cup of the cream, the corn syrup, butter, and sugar to 246 degrees F (firm ball); at this point the syrup will be golden. Remove from the heat and carefully swirl in the remaining 1/4 cup of cream and the vanilla. Use caution; this is very hot and it may splatter.
While the caramel is hot, dip and turn the apples into the caramel to coat and let the excess drip off. Dip the bottoms into the chopped nuts. Arrange the apples on a nonstick or waxed paper-lined cookie sheet and let cool.