Preheat oven to 375 degrees F. Line a baking sheet with parchment paper.
In a large bowl of a stand mixer, combine the butter and sugar and mix on medium-high speed using the paddle attachment for 2-3 minutes until light and fluffy.
Mix in the egg yolk and vanilla, scraping down the sides and bottom of the bowl as needed.
Add the flour, cornstarch, and salt and mix again until everything comes together in a nice dough. It may seem crumbly at first, but just scrape the bottom and sides of the bowl and keep mixing until the dough comes together.
Shape the dough into 1-tablespoon size balls and arrange 2 inches apart on the prepared baking sheet. Gently press in the center of each cookie with your thumb or the back of a ½ teaspoon measuring spoon to create and indentation. Fill with your favorite jam, warming the jam first for about 10 seconds so it is stirrable.
Bake for 9-11 minutes until set and just barely starting to turn golden around the bottom edges. Remove from the oven and cool for 10 minutes.
While the cookies cool, prepare the glaze by whisking together the powdered sugar, cream or milk, and vanilla in a medium bowl. Transfer to a ziplock bag and snip off one corner. Drizzle the glaze over cookies, then let set for 1-2 hours until the glaze has set up.