Preheat oven to 350°F and line an 8-inch cake pan.
Cream butter and sugar until light and fluffy. Add eggs and vanilla.
Mix dry ingredients separately and fold them into the wet mixture.
Add milk, mix gently, and pour into pan. Bake 28–32 minutes.
Make custard: Warm milk. Whisk yolks, sugar, and cornstarch. Temper with warm milk, cook until thick. Stir in butter and vanilla.
Cool custard completely.
Assemble: Spread custard over cooled cake. Add sliced strawberries. Brush with warmed jam.
Chill 30 minutes before slicing.