Preheat oven to 350°F. Line a large baking sheet with parchment paper.
In a bowl, cream together the softened butter and sugar until light and fluffy. Add flour and salt, mixing until a soft, crumbly dough forms.
Lightly flour a clean surface and roll the dough to about ¼ inch thickness. Use a Christmas tree-shaped cookie cutter to cut out trees. Gently transfer each tree to the prepared baking sheet.
Chill for 1 hour and 30 minutes.
Bake for 18–20 minutes, or until edges are lightly golden. Let cool completely on the pan before moving to a wire rack.
In a medium saucepan over medium heat, melt the butter. Stir in brown sugar, sweetened condensed milk, corn syrup, and salt. Cook, stirring constantly, for 8–10 minutes, until thickened and golden.
Line a new baking sheet with parchment. Place cooled shortbread trees on it, then carefully spoon a layer of warm caramel over each cookie, spreading to the edges. Let it set for 30 minutes at room temperature.
Melt chocolate chips and oil in the microwave in 30-second intervals, stirring until smooth. Spoon or spread chocolate over the caramel layer of each tree. Chill for 2–3 hours, or until the chocolate is firm.
Drizzle with melted chocolate and top with Christmas sprinkles. Let set, then serve or package for gifting.