Preheat oven to 350°F. Grease a 9-inch tart pan with removable bottom and place on a baking sheet.
In a stand mixer, beat 1 cup softened butter with ½ cup granulated sugar and ¼ cup brown sugar until pale and fluffy, about 3 minutes.
Mix in 1 tablespoon vanilla until well combined.
In a separate bowl, whisk together 2⅓ cups flour and ½ teaspoon salt. Add to butter mixture and mix on low until large clumps form.
Press two-thirds of the dough evenly into the prepared tart pan, including up the sides.
Spread 1 cup cherry preserves over the dough, leaving a ¼-inch border. Scatter 1 cup drained cherries evenly over the preserves.
Crumble the remaining dough into large pieces and distribute over the top, covering most of the surface.
Bake for 40-45 minutes until lightly golden and filling is bubbling. Cool completely in the pan.
For the icing, whisk together ½ cup powdered sugar, 1 teaspoon vanilla, 1 tablespoon melted butter, and 1 tablespoon milk. Add more milk if needed for drizzle consistency.
Drizzle icing over the cooled tart. Let set before slicing and serving.