In a medium bowl, stir together the flour, granulated sugar, baking powder, and salt.
Add the milk and melted butter to the dry ingredients and mix until a thick batter forms.
Fold the blueberries and lemon zest into the batter until evenly distributed.
Spread the batter into the bottom of a lightly greased slow cooker insert.
In a small bowl, beat the cream cheese with the powdered sugar, lemon juice, and vanilla until smooth.
Drop spoonfuls of the cream cheese mixture over the batter and use a knife to gently swirl it through the top layer.
Cover and cook on low for 2.5 to 3 hours, until the cobbler is set and the edges pull slightly from the sides.