Preheat oven to 350 degrees. Pulse flour, sugar, and salt in a food processor to combine. Add butter, and pulse until mixture resembles coarse meal. With machine running, gradually add milk, and process until dough forms.
Transfer dough to a lightly floured work surface. Slice off about 1 tablespoon dough. Using your hands, roll to 7 inches long and 1/2 inch in diameter. Place on a parchment-lined baking sheet. Repeat with remaining dough. Using a paring knife or kitchen scissors, make diagonal slits about 1/2 inch apart on both sides along the length of each breadstick. Gently stretch breadsticks (this will open the slits, creating "thorns").
Bake until pale golden brown, about 24 minutes. Transfer to a wire rack to cool completely.
Breadsticks can be stored in an airtight container at room temperature for up to 3 days.