Preheat the oven to 375 degrees F (190 degrees C).
Combine sugar, water, and cornstarch in a saucepan. Cook over medium heat, stirring constantly, until very thick, about 5 minutes. Remove from heat and mix in strawberries. Pour mixture into a 9×13-inch baking dish.
Stir flour, baking powder, and salt together in a small bowl. Set aside.
Cream butter and sugar in a bowl with an electric mixer until light and fluffy. Beat in eggs and vanilla extract. Add flour mixture and stir with a spatula just until ingredients are combined. Drop batter by rounded tablespoons over the strawberry mixture. Try to cover as much filling as possible.
Bake in the preheated oven until topping is golden brown and filling is bubbling, 35 to 40 minutes. A toothpick inserted into the topping should come out clean. Remove cobbler from the oven and let cool. Serve warm or at room temperature.