Heat the oven to 375 °F and grease a 1.8-liter casserole dish. The suggested oval dish is 11 x 8½ x 2, and a similar size helps the cobbler bake evenly.
Toss the diced strawberries with the sugar in a medium bowl, then let them stand while you make the batter. They should look glossy and syrupy as the sugar pulls out their juices.
Whisk the flour, baking powder, sea salt, and sugar together in a large bowl. Mixing the dry ingredients first helps the leavening distribute evenly through the crust.
Pour in the warm milk, vanilla extract, and melted butter. The mixture will start to look thick and creamy almost right away.
Stir just until the batter comes together. A few lumps are a good sign here, and the texture should look like thick pancake batter.
Spread the batter evenly in the prepared dish. It will be thick, so use a spatula to nudge it into the corners if needed.
Spoon the strawberries over the batter with a slotted spoon and leave the excess syrup behind in the bowl. Keep the layers separate and do not stir, or the cobbled top will not form properly.
Bake on the middle rack for 35 to 40 minutes. The top should be golden brown, and you should see bubbling fruit around the edges.
Take the cobbler out of the oven and let it rest before serving. The filling will thicken as it sits, which makes it easier to scoop.
Spoon into bowls and serve warm, with vanilla ice cream if you like. The contrast of warm fruit and cold ice cream is hard to argue with.