Preheat the oven to 425 degrees F (220 degrees C). Line a baking sheet with parchment paper.

Melt butter in a small saucepan over medium heat. Stir continually, letting foam dissipate, just until butter begins to brown, 2 to 3 minutes. Remove from heat.

Whisk self-rising flour and ¼ cup white sugar together in a bowl. Add milk, ¼ cup cream, and toasted butter; mix just until combined.

Turn dough out onto a floured surface; press or roll into a rectangle about 1-inch thick. Cut in half lengthwise, then cut each half into three portions. Place shortcake portions on the prepared baking sheet. Brush with cream; sprinkle with sugar.

Bake in the preheated oven until golden brown, 15 to 18 minutes. Transfer shortcakes to a rack to cool completely.

Sprinkle sliced strawberries with ¼ cup sugar; stir until sugar begins to dissolve. Refrigerate until juice from berries is extracted, about 1 hour.

Beat ¾ cup cream, 1 tablespoon sugar, and few drops vanilla extract in a bowl with an electric mixer until soft peaks form.

Split shortcakes in half; place bottom half in a bowl. Spoon strawberries and juice over shortcake half; top with shortcake top. Spoon more strawberries and juice over shortbread. Finish with a dollop of whipped cream.