Cream cold butter and sugar until light and fluffy, 2-3 minutes.
Beat in egg yolk and vanilla extract.
Whisk flour and salt; fold into wet ingredients until just combined.
Chill dough 20-30 minutes.
Roll into 1-tablespoon balls, press a well into each (pinch cracks closed), and fill with 1/2 tsp smooth jam.
Preheat oven to 350°F. Bake 12-14 minutes, until edges are just set and barely golden.
Cool completely. Whisk powdered sugar, vanilla, and milk into a slow-ribbon icing; drizzle over cookies and let set 10 minutes.