Preheat oven to 350 degrees.
Combine 2 ½ cups blueberries and 1 tablespoon cornstarch in a food processor, and process until smooth. Place puree in a small saucepan; bring to a boil. Cook 6 minutes or until slightly thick, stirring constantly. Cool before using in cupcakes.
Cream together butter & sugar. Beat in eggs one at a time. Add vanilla. Add flour mixture, alternating with milk on medium speed with an electric mixer. . Stir in puree until incorporated.. Using an ice cream scoop, add into paper liners until ½ to ⅔ full. Bake for 15-18 minutes. Cool 5 minutes in pans then remove and place on wire racks to cool completely.
Cream together the cream cheese and butter until creamy. Mix in the vanilla, then gradually stir in the confectioners' sugar. Store in the refrigerator after use.