Heat oven to 375° F.
In a skillet, over medium heat, melt 2 tablespoons of the butter. Add the jalapeño and scallions. Cook for 3 minutes. Add the corn and broth. Increase heat to medium-high and cook for 4 minutes. Turn off heat. Stir in the cream, 1 teaspoon of the salt, and the pepper. Pour into a buttered 9-by-13-inch baking dish.
In a large bowl, combine the flour, baking powder, and the remaining salt. Using your fingertips, add the remaining butter, cut into small pieces. Mix until it resembles crumbs. Stir in the thyme and milk. Drop heaping spoonfuls of the batter on top of the corn mixture. Bake for about 50 minutes. Garnish with fresh thyme, if desired.
Make Ahead: Prepare the filling and the biscuits the night before. Refrigerate them separately, leaving the biscuit dough in the bowl. Assemble the cobbler just before baking, then allow an extra 5 minutes in the oven.