Preheat the oven to 350°F. Grease two 9-inch round cake pans and line the bottoms with parchment paper.
In a large mixing bowl, cream the butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract and lemon zest.
In a separate bowl, whisk together the flour, baking powder, and salt.
Add the dry ingredients and milk to the butter mixture alternately, beginning and ending with the dry ingredients. Mix until smooth and well combined.
Divide the batter evenly between the prepared cake pans.
Bake for 20 to 25 minutes, or until a toothpick inserted into the center comes out clean.
Cool the cakes in the pans for 10 minutes, then turn them out onto wire racks to cool completely.
To make the strawberry filling, combine the sliced strawberries, sugar, and lemon juice in a saucepan over medium heat. Cook until the berries release their juices and begin to soften.
Stir in the cornstarch slurry and cook for 1 to 2 more minutes, until the mixture is glossy and slightly thickened. Remove from the heat and let cool slightly.
In a chilled mixing bowl, whip the heavy cream, powdered sugar, vanilla bean paste, and a pinch of salt until medium-stiff peaks form.
Place one cake layer on a cake stand or serving plate. Spread a generous layer of whipped cream over the top, then spoon over a thick layer of strawberry filling.
Place the second cake layer on top. Frost the top and sides with the remaining whipped cream.
Garnish with fresh strawberries, if desired, and serve.