In a large bowl, add the sliced pears, 3/4 cup of the brown sugar, 1 teaspoon of the ground cinnamon, the nutmeg, and the salt. Stir to coat the pears thoroughly. Set aside.
In a medium bowl, whisk together all-purpose flour, remaining 1 cup brown sugar, baking powder, and remaining 1 teaspoon of ground cinnamon.
Add the buttermilk and vanilla extract, stirring just until combined.
Preheat the oven to 350°F. Pour the melted butter into a 9x13-inch baking dish. Pour the batter over the melted butter without stirring.
Arrange the pears evenly over the batter. Bake in the preheated oven for 40-45 minutes, until the top is golden brown.
Let the cobbler cool for at least 15 minutes before serving. Serve with whipped cream or a scoop of vanilla ice cream.