Add 1 ¼ cups flour, granulated sugar, 1 ½ tablespoons poppy seeds, baking powder and salt to a food processor, and pulse a few times to combine. Add butter and pulse until small crumbs form. Stream milk and vanilla into flour mixture while machine is running. Pulse until dough is fairly smooth.
Wrap dough in plastic and transfer to a small baking sheet. Chill until firm, at least 1 hour and up to 3 days.
Heat the oven to 350°F. Roll dough to about ¼-inch thick. Use a bench scraper or long knife to cut the dough crosswise into 1/4-inch-thick strips that are about 3 inches long. Transfer half the dough to the refrigerator while you work with the other half. Using the palms of your hands, gently roll each strip on a lightly floured work surface until it is 6 inches long. Transfer strips to silicone mat-lined baking sheets, keeping them as straight as possible and spacing them about 1 1/2 inches apart. Repeat with remaining dough.
Bake until golden on edges and bottom, 10 to 12 minutes. Let cool a few minutes on the baking sheets, then transfer to wire racks to cool completely.