Place 1 cup of strawberries in a large bowl and smash (macerate) them with 1/4 cup of sugar. Use the back of a ladle or a wooden spoon to do this. Mix with the rest of the berries into the bowl and chill until ready to serve.
Preheat oven to 425 degrees F. Combine the flour, cornmeal, baking powder, salt, and 1/4 cup sugar in the food processor. Pulse to mix.
Chop the cold butter into cubes and add to the processor. Pulse the processor several times until the pieces are the size of peas. Add 1 egg and 1/2 cup whole milk to the food processor. Pulse one or two times, until just combine. You still want to be able to see butter clumps.
Dump the dough onto a floured work surface and shape with your hands into a rectangle about 3/4- to 1-inch thick. Use a 3-inch cookie cutter to cut out 6-8 shortcakes.
Place them on a parchment paper-lined baking sheet. Brush the shortcakes with milk and sprinkle the extra 2 tablespoons of sugar over the tops.
Bake for 12-14 minutes, until golden. Cool the shortcakes for just a few minutes.
Whip the heavy cream in an electric mixer, with the vanilla and 3 tablespoons sugar, until soft peaks form.
Find a crack in the side of each shortcake and gently separate them into tops and bottoms. Spoon berries over the bottom half of each shortcake, add a large dollop of whipped cream, and place the shortcake top on the cream. Serve immediately.