Preheat the oven to 350°F. Grease a 9x13-inch baking dish.
In a medium bowl, whisk together the brown sugar, ½ cup granulated sugar, 2 tsp cinnamon, salt, vanilla, and hot water until mostly dissolved. Set aside.
In a large bowl, whisk together the flour, 1½ cups granulated sugar, baking powder, salt, 2 tsp cinnamon, and cream of tartar.
Stir in the milk, melted butter, and vanilla just until a thick batter forms.
Spread the batter evenly into the prepared baking dish.
Slowly pour the cinnamon filling evenly over the batter. Do not stir.
In a small bowl, combine the remaining ½ cup granulated sugar and 2 tsp cinnamon.
Sprinkle the cinnamon sugar evenly over the top.
Bake for 45–50 minutes, until the top is golden brown and the center is mostly set with just a slight jiggle.
Let the cobbler cool for at least 20 minutes before serving. The filling will continue to thicken as it rests.
Serve warm with vanilla ice cream if desired.