Preheat oven to 400º. Grease 2 quart baking dish with butter.
In a medium saucepan, combine sugar, cornstarch, water, and strawberries. Cook over medium heat, stirring constantly, until thick and hot. Pour mixture into the prepared baking dish. Dot with 2 tablespoons butter.
Dough: In a bowl, combine flour, baking powder and salt. Blend in 3 tablespoons butter. Stir in half and half. Mixture will be soft. When you spoon dough onto the berries, it will probably sink to the bottom. Just try to spread as best you can. It comes out good in the end.
Bake for about 20 to 25 minutes in the oven. When almost done, mix the 1/4 cup butter and 1/4 cup brown sugar and heat them in a saucepan or in the microwave. When heated, brush it on top of the cobbler and bake another 5 to 10 minutes.