1. Preheat oven to 350 degrees. In a large bowl, using an electric mixer, beat butter, 1 cup brown sugar, and lemon zest until light and creamy. Add vanilla and egg and beat to combine, scraping down bowl as needed. In a medium bowl, whisk together flour, baking powder, baking soda, and salt. With mixer on low, beat in flour mixture in 3 additions, alternating with milk and ending with flour mixture (scrape bowl as needed). Beat well to combine.

2. Drop batter in 2-tablespoon mounds, about 2 inches apart, onto 2 parchment-lined baking sheets. Bake until puffed and pale golden around edges, 17 to 19 minutes, rotating sheets halfway through. Let cakes cool completely on sheets on wire racks.

3. In a large bowl, whip cream and 3 tablespoons brown sugar to soft peaks. In a small bowl, mash raspberries with a fork, then fold into whipped cream. Divide raspberry cream evenly among bottoms of half the cakes, then sandwich with remaining cakes.