1 tablespoon canola or other flavorless vegetable oil
1 1/2 cups heavy whipping cream
1 cup light corn syrup
3/4 cup sugar
3 tablespoons unsalted butter, softened
2 teaspoons pure vanilla extract
1 1/2 cups toasted and coarsely chopped walnuts or unskinned almonds
Line an 8-inch-square metal baking pan with foil, extending the foil over the sides of the pan. Thoroughly coat the foil with the canola oil.
In a heavy 3-quart saucepan, combine the cream, corn syrup and sugar. Stir continuously over moderate heat with a long-handled wooden spoon until the sugar is dissolved, about 5 minutes. Using a pastry brush dipped in warm water, brush down the side of the pan twice to prevent crystallization.
Raise the heat to moderately high and place a candy thermometer in the pan. Continue to cook the syrup, stirring constantly, until the temperature registers 250°, about 30 minutes.
Remove the saucepan from the heat and quickly stir in the butter, vanilla and nuts. Pour the caramel into the prepared pan and let cool to room temperature on a rack, at least 2 hours.
Use the ends of the foil to lift the caramel from the pan. Peel the foil off the back of the caramel. Coat the blade of a chef's knife with oil. Cut the caramel into 8 equal strips, then cut each strip into 8 pieces. Arrange the caramels, without touching one another, between sheets of wax paper, or wrap them individually in wax paper.
Store the caramels in an airtight container at room temperature for up to 2 weeks.