Preheat oven to 375 degrees F (190 degrees C). Line baking sheets with parchment paper.
In a large bowl, cream butter with brown sugar and 1/3 cup white sugar. Blend in the vanilla and milk. Mix in the flour and corn starch. Stir in the mini chocolate chips.
Form the dough into 1 inch balls, and roll in the remaining white sugar. Place on the prepared cookie sheet, about 1 1/2 inches apart. Use your finger or thumb to press straight down into the center of each ball, making a well for the jam. Neatly fill each cookie with a small amount of jam.
Bake in preheated oven for 13 to 15 minutes, or until cookies are just beginning to turn golden around the edges. Let cookies cool before eating.
