Position rack in center of oven and preheat to 350°F. Generously grease the sides of a 9-inch round cake pan.
Cut the 3 tablespoons butter into small pieces and place in the cake pan. Place the pan in the oven for a minute or two until the butter is just melted.
Remove the pan from the oven and swirl the melted butter to coat the bottom of the pan. Evenly sprinkle the brown sugar over the melted butter to form a thin layer at the bottom of the pan. Arrange the sliced strawberries in a single layer over the brown sugar, making sure the slices are touching or slightly overlapping.
In a medium bowl, whisk together the flour, baking powder, and salt; set aside. In a large bowl, use an electric mixer to beat the softened butter and sugar until fluffy. Scrape the bowl and blend in the egg and vanilla. Beat on high for 3 minutes, scraping the bowl occasionally. With the mixer on low speed, gradually blend the flour mixture into the wet mixture, alternating with the milk until just combined.
Scrape the batter into the pan and carefully spread over the strawberries. Bake for 28 to 32 minutes or until toothpick inserted in the center of the cake comes out clean.
Set the cake pan on a cooling rack and cool the cake in the pan for 3 minutes. Carefully run a thin knife or spatula around the edge of the cake pan, then lay a cake platter on top of it. Pressing down on the platter, quickly invert the pan so that it's upside-down on the platter. Wait for 1 minute and then slowly and carefully lift the cake pan from the top of the cake. If any berries stick to the pan, place them back on the top of the cake.
Serve cake warm or at room temperature. Cool completely before covering and storing leftovers at room temperature for up to three days.