Preheat the oven to 425° F.
To prepare the filling: In a large oven safe skillet, combine the apples, butter, brown sugar, cinnamon, allspice, nutmeg and salt over medium heat. Cook for several minutes, stirring, until the apples have lightly caramelized and are soft but not mushy.
Mix together the lemon juice and cornstarch and stir it into the apple mixture. Remove from the heat.
Whisk together the flour, 2 tablespoons granulated sugar, 1 teaspoon cinnamon, baking powder, and salt.
In a liquid measuring cup, stir together the half and half, melted butter and vanilla extract.
Pour the liquid ingredients into the dry and stir until just combined.
In a separate small bowl, mix together the remaining 1 tablespoon sugar and 1/4 teaspoon cinnamon.
For two smaller cobblers, divide the apple mixture evenly among two 5-inch oven safe skillets. For one large cobbler, leave the apples in the same skillet.
Spoon the dough evenly on top of the apples and use a spatula to gently spread it out. The apples do not need to be completely covered. Sprinkle the cinnamon sugar mixture evenly on top of the dough.
Bake for 18 – 22 minutes or until the sides are bubbly and the dough has cooked through. Serve hot with ice cream on top.