Lightly grease an 8x8-inch or 9x9-inch baking dish.

Combine the butter, corn syrup, and granulated sugar in a medium saucepan over medium heat.

Cook while stirring steadily until the ingredients melt together and the mixture just begins to simmer. Remove from the heat.

Stir in the powdered sugar, powdered milk, vanilla extract, and 1 tablespoon milk. Continue mixing until a smooth, very stiff dough forms.

Press the nougat mixture into the prepared baking dish in a roughly even layer.

Let the nougat cool completely until firm.

Cut the nougat into 8 equal pieces. Roll each piece between your palms into a log about 6 inches long.

Place the logs on a parchment- or wax-paper-lined tray and freeze for at least 1 hour.

Place the caramel candies and remaining 2 tablespoons milk in a heatproof bowl set over a saucepan of gently simmering water.

Heat while stirring frequently until the caramel is completely melted and smooth.

Spread the chopped pecans in a shallow dish or rimmed baking sheet.

Working with one frozen log at a time, dip it into the melted caramel and turn until completely coated.

Allow the excess caramel to drip off, then roll the log in the chopped pecans, pressing gently so they adhere.

Return the coated log to the lined tray and repeat with the remaining pieces.

Let the pecan logs set completely before slicing or serving.