Preheat oven to 350°. Grease a 8 x 8 baking pan and set aside.
Add the softened butter and sugar in a large mixing bowl. Cream together with an electric mixer on medium speed.
Add the egg and vanilla extract and mix for an additional 30 seconds. Set aside.
In a medium mixing bowl, whisk together the flour, baking powder and salt. Mix in half of the dry ingredients to the creamed butter.
Add in 1/4 cup of the milk and stir until mixed. Add the remaining flour and the remaining milk. Stir again until all of the ingredients are wet.
Transfer the batter to your greased pan, and even the batter out.
In a small bowl, whisk together 1/4 cup flour and 1/4 cup sugar. With a pastry blender or using 2 forks, cut in the chilled butter slices until crumbly.
Place a layer of strawberries on top of the batter, cut side facing down.
Sprinkle the crumbly mixture on top of the strawberries.
Bake at 350° for 45 minutes, or until an inserted toothpick comes out clean.
Let the strawberry cobbler cool down.
Serve, and enjoy with ice cream!