Preheat the oven to 350°F. Grease and flour a deep 8-inch round cake pan.

In a medium bowl, sift together 1 cup all-purpose flour, 1 teaspoon baking powder, and ¼ teaspoon kosher salt. Set aside.

In a large mixing bowl, add 4 large eggs. Beat on medium speed for 1 minute. Gradually add 1 cup granulated sugar and ½ teaspoon pure vanilla extract. Continue beating for 7 to 8 minutes, until the mixture is thick, pale, and holds ribbons.

Gently fold the dry ingredients into the egg mixture in three additions, alternating with ¼ cup melted butter and ¼ cup whole milk, starting and ending with the dry ingredients. Fold carefully to avoid deflating the batter.

Pour the batter into the prepared pan and smooth the top. Bake for 30 to 35 minutes, until a toothpick inserted into the center comes out clean.

Let the cake cool in the pan for 10 minutes. Turn out onto a wire rack and cool completely.

In a clean mixing bowl, whip 1 cup heavy whipping cream until stiff peaks form. Set aside.

In another bowl, add 8 ounces mascarpone cheese, 1 cup powdered sugar, lemon zest, lemon juice, and 1 teaspoon pure vanilla extract. Beat until smooth and creamy.

Gently fold the whipped cream into the mascarpone mixture until fully combined. Reserve ½ cup of the lemon cream for the exterior of the cake.

Once completely cooled, use a long serrated knife to slice the cake horizontally into two even layers.

Place the bottom layer on a serving plate. Spread the lemon cream filling evenly over the top, leaving the reserved portion aside. Place the second layer on top.

Spread the reserved ½ cup lemon cream around the sides of the cake. Gently press the vanilla cookie crumbs into the sides to coat.

Refrigerate the cake for at least 2 hours to set.

Just before serving, dust the top lightly with powdered sugar.