Preheat oven to 375°F. Butter, or spray with cooking spray, a large 12x18-inch rimmed baking sheet tray.
In a medium bowl, add the cherry pie filling, lemon juice, and almond extract for the cherry filling. Stir to combine. Set aside.
In a second medium bowl, add the apple pie filling, fresh lemon juice, and cinnamon for the apple filling. Stir to combine. Set aside.
In a third medium bowl, add the blueberry pie filling, fresh lemon zest, and fresh lemon juice for the blueberry filling. Stir to combine. Set aside.
To make the cobbler topping add, to a large mixing bowl, the all-purpose flour, baking powder, salt, brown sugar, granulated sugar, and the small cubes of cold unsalted butter. Using a pastry cutter, cut the butter into the flour mixture until it resembles coarse crumbs. The butter should be little ‘pea-sized’ pieces.
Pour the cold heavy cream into the flour mixture and gently mix it in using your hands or a wooden spoon just until all the heavy cream has been incorporated. You will want to squeeze the dough mixture into chunks, or large crumbles, with your hands. This is what gives your sheet pan cobbler that “cobblestone” look to the topping. Do not overmix the dough, or it will become tough when baked.
Transfer your fruit fillings to the prepared rimmed sheet tray. You will start with placing the cherry filling on the left ⅓ of the tray, then in the center ⅓ of the tray, place the apple filling and then fill the final ⅓ of the tray with the blueberry filling.
Using your hands, you will want to place your chunks of dough randomly all over the top of your fruit fillings. Leave a few little gaps between the dough so you can see the varieties of fruit peeking through the topping when baked.
Bake for 30 minutes or until the fruit is bubbly and the cobbler dough is lightly golden.