Preheat oven to 350°F.
Grease a 9-inch round cake pan with butter or nonstick spray.
Prep the strawberries:
Toss sliced strawberries with brown sugar. Let sit 5–10 minutes while making the batter.
Make the cake batter:
Brown 10 tablespoons of unsalted butter in a light-colored saucepan over medium heat, stirring often, until golden brown and nutty-smelling, 5 to 7 minutes.
Immediately pour into a large heatproof bowl to cool slightly—you’ll be left with about 8 tablespoons of browned butter.
Add brown sugar and whisk together. Whisk in egg, buttermilk, and vanilla until smooth.
In a separate bowl, whisk flour, baking powder, and salt. Fold into wet ingredients until just combined.
Assemble:
Pour batter into the prepared pan and smooth the top.
Spoon the strawberries evenly over the batter, leaving the juices behind. (you can save them to spoon over the top of the finished cake, or add to iced tea or seltzer water for a refreshing beverage on the side)
Bake:
Bake for 30 to 35 minutes, or until the top is golden and the cake is set in the center.
Cool slightly and serve:
Spoon warm portions into bowls and top with a dollop of Greek yogurt, whipped cream, or crème fraîche. Drizzle reserved juices on top, if desired.