In a large bowl, with an electric mixer on medium speed, beat butter, sugar, and vanilla until smooth. Stir or beat in flour until dough is no longer crumbly and starts to come together into a ball.
Divide dough into thirds. On a lightly floured surface, roll each portion into a 9-inch-long rope about 1 inch thick. Place ropes 3 inches apart on a buttered or cooking parchment-lined 12- by 15-inch baking sheet. Press your finger into dough to make 1/2-inch-wide indentations at 1-inch intervals along each rope. Spoon about 1/4 teaspoon jam into each indentation.
Bake ropes in a 350° oven until edges are lightly browned, 12 to 15 minutes. Let cool on baking sheet.
Place white chocolate in a zip-lock plastic bag, pushing to one corner; seal bag. Immerse corner of bag in a cup of hot water until chocolate is melted. Dry bag, then, with scissors, cut off the tip of the corner. Squeeze bag to drizzle white chocolate decoratively across ropes. Chill until chocolate is firm to touch, about 1 hour, then cut each rope diagonally into 12 slices.
Note: Nutritional analysis is per cookie.