Apple and Blackberry Polenta Cobbler

INGREDIENTS

• 3 baking apples (such as Honeycrisp or Pink Lady), peeled, cored, cut into 1/4-inch wedges
• 1 10-ounce package frozen blackberries (about 2 cups), thawed
• 1/3 sugar
• 3 cornstarch
• 3 honey
• 2 unsalted butter, cut into 1/2-inch pieces
• 2 fresh lemon juice
• 1/2 medium-grind polenta or cornmeal (not quick-cooking)
• 2 baking powder
• 3/4 kosher salt
• 1 1/2 all-purpose flour plus more for work surface
• 1/4 sugar plus more for sprinkling
• 6 (3/4 stick) chilled unsalted butter, cut into 1/2-inch pieces
• 1 heavy cream plus more for brushing