In a blender, puree beets with liquid until smooth, scraping down sides with a spatula as needed. (You should have about 1/2 cup puree.)
Preheat oven to 350ºF. Grease an 8-inch square glass baking dish. In a heatproof bowl set over a saucepan of simmering water, melt butter and 4 oz. chocolate, stirring occasionally, until chocolate is smooth. Remove bowl from heat; whisk in sugar. Whisk in eggs 1 at a time until incorporated. Stir in pureed beets, vanilla and salt. Fold in all but 2 Tbsp. flour. Toss remaining 2 Tbsp. flour with remaining 2 oz. chocolate chips and cherries. Fold into batter until just combined.
Pour batter into prepared baking dish and bake until just set, 30 to 35 minutes. Let cool completely in dish on a wire rack. For easiest cutting, refrigerate for at least 1 hour, then divide into 12 squares.