Adjust oven rack to middle position and heat over to 350 degrees. Line rimmed baking sheet with parchment paper. Combine strawberries, 1/4 cup sugar and 1/4 tsp. salt in bowl. Whisk water and cornstarch together in second bowl; add to strawberry mixture and toss until strawberries are evenly coated.
Transfer strawberry mixture to 8-inch square baking dish and place dish on prepared sheet. Bake until filling is bubbling around sides of dish, 35 to 40 minutes (1 hour if using frozen strawberries), stirring and scraping bottom of dish with rubber spatula halfway through baking.
Remove sheet from oven and stir filling, scraping bottom of dish with rubber spatula. Whisk flour, baking powder, remaining 3/4 cup sugar and 1/4 tsp. salt together in bowl. Whisk in milk, melted butter and vanilla until smooth. Starting in corner of dish, pour batter evenly over filling.
Bake until surface is golden brown and toothpick inserted in center comes out with no crumbs attached, 35 to 40 minutes, rotating dish halfway through baking. Let sonker cool on wire rack for 15 minutes. Serve
Blueberry Sonker: Substitute 2 pounds (6.5 cups) fresh or frozen blueberries for strawberries.
Peach Sonker: Substitute 2.5 pounds peaches, peeled, halved, pitted and cut into 1/2-inch-thick wedges or 2 pounds frozen sliced peaches (break up any slices that are frozen together) for strawberries.