Preheat the oven to 350 F, and position a rack in the center of the oven.
In a bowl, combine the sliced strawberries with 1/4 cup of the sugar. Set aside to macerate for several minutes while you make the cake batter, until the strawberry juices become syrupy.
Melt the butter, then brush about 2 teaspoons of the melted butter over the bottom and sides of your pan. I used a 7x11 inch oval baking dish, but a 9x9 inch or 10x10 inch square baking dish will also work. Baking times will vary slightly for different pan sizes.
In a bowl, whisk together the rest of the melted butter with 1/2 cup of the sugar, the milk, egg and vanilla.
Sift the flour, baking powder and salt together, then add the dry ingredients to the wet ingredients and whisk until smooth, about 15 seconds.
Pour the batter into the prepared pan. Spoon the sugared strawberries over the batter, including all the juice and syrup left at the bottom of the bowl. Sprinkle the remaining 1 tbsp sugar over the strawberries and cake batter.
Bake the cake for about 40 minutes, or until a cake tester or sharp knife inserted in the center comes out clean.
Let the cake cool for 10 minutes, then serve warm with whipped cream or ice cream. When the cake is warm from the oven, the edges will be crisp and slightly chewy, with a soft, cakey center.