Preheat oven to 350°F. Spray mini muffin pans with floured nonstick cooking spray.
Place butter in the bowl of a stand mixer fitted with the paddle attachment. (You can also use a hand mixer.) Beat butter until it’s smooth, then beat in powdered sugar. Beat in vanilla and salt and then slowly mix in flour. Beat until batter forms.
Drop 1 tablespoon balls of cookie dough into each mini muffin pan cavity. Press it up the sides of the pan, creating a crust. I find it's easiest to use the back of a wooden spoon or thick handle/glass to press the cookies (rather than using my fingers).
Drain blueberries well if thawed. Toss with sugar, cornstarch, and lemon juice. Evenly divide between the cookies, adding some of the liquid that collects in the bottom of the berry bowl but not too much.
Bake for 20-25 minutes, or until the sides start to get golden in color. Cool completely before removing from pan.
To top: stir white chocolate chips and vegetable oil in a small microwave safe bowl. Heat on 50% power in 30 second increments, until melted and smooth. Add to a small sandwich bag with the tip cut off and drizzle over cookies. Let set before serving.
Store in an airtight container for up to 3 days. Or freeze for up to 3 months.