Combine strawberries, sugar, cornstarch, and lemon juice in a saucepan and cook until berries soften and juices thicken. Gently mash the mixture while cooking to achieve a jam-like consistency. Stir in butter at the end and let the filling cool completely before using.
Cream butter and sugar together until fluffy, then mix in eggs and vanilla until smooth. Whisk dry ingredients separately and gradually add them to form a thick dough. Chill the dough so it’s easier to handle and shape.
Scoop dough into balls, split each portion, and form small wells to hold filling. Spoon in the cooled jam, cover with dough, and seal edges so filling stays inside. Chill briefly, then bake until cookies turn lightly golden on edges.
Whisk powdered sugar, milk, corn syrup, and vanilla until smooth and slightly thick. Spread icing over cooled cookies and immediately sprinkle decorations on top. Allow icing to set completely before serving or storing.