Preheat your oven to 375°F (190°C). Spray a 9x13-inch baking dish with non-stick spray to prevent sticking. This creates the perfect base for your peach cobbler.
In the prepared baking dish, add the frozen sliced peaches, 1 cup granulated sugar, 1 cup packed light brown sugar, vanilla and almond extracts, 1/2 tablespoon ground cinnamon, 1/2 teaspoon ground nutmeg, cornstarch, cream of tartar, 4 tablespoons room temperature butter, 2 tablespoons water, and lemon juice. Mix everything together well until the peaches and ingredients are fully coated. Cover the dish with foil and bake in the preheated oven for 20 minutes to let the peaches release their juices and the flavors meld together.
While the peaches are cooking, prepare the cobbler dough. In a large mixing bowl, combine the all-purpose flour, 1/2 cup granulated sugar, 1/2 cup light brown sugar, baking powder, salt, and 1/2 tablespoon of the cinnamon. Cut the cold stick of butter into small pieces and work it into the dry mixture using a pastry cutter or your hands until the mixture resembles coarse meal or crumbles. Gradually add the 1/4 cup boiling water and stir until just combined, forming a drop biscuit-like dough. I like to handle the dough gently to keep it tender and ensure a light, fluffy cobbler topping.
Carefully remove the baked peaches from the oven after 20 minutes. Using a spoon, drop the cobbler dough mixture over the peach filling in golf ball-sized portions, leaving a little space between each dough ball so the biscuit topping can cook through. The peaches will not be completely covered, which allows for an attractive, rustic look and lets some of the filling bubble up between the biscuits.
In a small bowl, combine 3 tablespoons granulated sugar with the remaining 1/2 tablespoon ground cinnamon. Sprinkle this mixture evenly over the dough balls in the baking dish. For an extra-sparkly crust, I like to be generous with the cinnamon sugar, which gives the cobbler a wonderful aroma and sweet crunch after baking.
Place the assembled cobbler back in the oven, uncovered, and bake for an additional 30-45 minutes. Bake until the biscuit topping is golden brown and cooked through. Check after 30 minutes and continue baking if needed. Once done, remove the cobbler and let it cool slightly before serving. Enjoy your homemade peach cobbler warm, perhaps with a scoop of vanilla ice cream!