For the basil whipped cream: Bring the cream to a simmer in a small saucepan. Remove from the heat and stir in the basil. Let sit 30 minutes, then strain and refrigerate until cold, at least 2 hours.
For the cake: Preheat the oven to 350 degrees F with a rack in the middle. Butter and flour a 9-inch cake pan and line the bottom with a circle of parchment.
Stir together the flour, baking powder and salt in a medium bowl. Beat the butter and 1/2 cup of the granulated sugar on high speed in a mixer fitted with the paddle attachment until light and fluffy, about 3 minutes, scraping down the sides occasionally. Reduce the speed to low and mix in half of the flour mixture. Add the milk and vanilla and mix to combine. Add the remaining flour mixture and mix just until smooth.
In a clean mixer bowl, whisk the egg whites and remaining 1/4 cup granulated sugar to firm peaks. Stir about a third of the egg whites into the batter to lighten it, then gently fold in the remaining egg whites. Spread the batter into the prepared pan. Bake until a tester in the center comes out clean, about 25 minutes. Cool in the pan on a rack for about 10 minutes, then remove from the pan and cool completely.
For the strawberries: Combine the strawberries and granulated sugar in a medium bowl. Toss well and refrigerate until the sugar dissolves and the berries become juicy, about 30 minutes. Taste and add a little more sugar if needed. When ready to serve, add the basil and toss.
Put the chilled cream in the bowl of a mixer fitted with the whisk attachment. Whisk on medium until foamy, then gradually add the confectioners' sugar and increase the speed to high. Whisk to form soft peaks, about 2 minutes. Whisk in the vanilla.
Split the cake horizontally with a serrated knife into 2 thinner layers. Place the bottom layer on a serving platter. Top with half of the whipped cream and then half of the strawberries. Add the top layer, cut-side down. Top with the remaining whipped cream and strawberries. Garnish with basil sprigs and serve immediately.