Melt 2 tablespoons of the butter in a medium skillet over medium-high heat. Add the pineapple and brown sugar and cook, stirring occasionally, until the pineapple is slightly softened and golden brown, about 6 minutes.
Whisk the flour, cornmeal, baking powder and salt together in a medium bowl. In a separate bowl, beat the remaining 1 stick butter and the granulated sugar together with an electric mixer on medium-high speed until light and fluffy, about 3 minutes. Add the egg and vanilla and beat until incorporated. Reduce the speed to low and add half of the flour mixture, followed by the milk and then the remaining flour, beating just until incorporated.
Divide the caramelized pineapple among six 8-ounce Mason jars, pressing with a spoon to compact the pineapple slightly. Divide the batter among the jars (a little over 1/3 cup per jar).
Set the jars on a baking sheet and bake until a wooden pick inserted into the center comes out clean, 25 to 30 minutes. Transfer to a rack to cool slightly.
Top each jar with a spoonful of Cherry Glaze.
Add the cherry preserves and pineapple juice to a small saucepan. Heat over medium heat until the jam cooks down slightly.