Lemon Snack Cake with Raspberry-Cream Cheese Frosting

Name: Lemon Snack Cake with Raspberry-Cream Cheese Frosting
Prep time: 35 min
Total time: 35 min
Cuisine: American
Ingredients: 1.5 sticks unsalted butter, room temperature, plus more for pan; 2 cups unbleached all-purpose flour, plus more for pan; 1 teaspoon baking powder; 0.5 teaspoon baking soda; 1 teaspoon kosher salt; 0.667 cup whole milk; 1 tablespoon finely grated lemon zest, plus ⅓ cup fresh juice; 1 cup granulated sugar; 2 teaspoons pure vanilla paste or extract; 2 large eggs, room temperature; 6 ounces cream cheese, room temperature; 6 tablespoons unsalted butter, room temperature; 1 cup plus 2 tablespoons confectioners' sugar, sifted; 0.25 ounce freeze-dried raspberries (⅓ cup), finely ground; Fresh raspberries, for serving