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Spray a 9 by 9-inch glass baking dish with nonstick spray and set aside.
In the bowl of a stand mixer, with the paddle attachment, beat together the butter and sugar on medium speed until light and fluffy, approximately 1 minute. Add the egg and beat until well incorporated, approximately 30 seconds. Add 1/3 of the flour mixture and beat on low speed just until incorporated and then add 1/3 of the milk and beat until incorporated. Repeat, alternating flour and milk until everything has combined. Gently stir in the blueberries and pour the mixture into the prepared baking dish.