Preheat the oven to 350°F (177°C). Line two 8-inch round cake pans with parchment paper and grease the sides. In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. In a large bowl, cream together the butter and granulated sugar until fluffy. Add the vegetable oil and eggs one at a time, mixing well. Gradually add the dry ingredients to the wet mixture, alternating with the milk until combined. Pour the batter into the prepared pans and bake for 25-30 minutes. Cool in pans for 5 minutes before transferring to a wire rack.
For the crumb topping, spread flour on a parchment-lined baking sheet and bake for 5 minutes. Let it cool. Whisk together the cooled flour and powdered sugar. Cut in cold butter until crumbly, then add lemon zest and vanilla extract; refrigerate for 1 hour.
For the filling, whip the heavy whipping cream to stiff peaks. In another bowl, combine mascarpone cheese, powdered sugar, lemon zest, and lemon juice until smooth. Fold in the whipped cream gently. Chill.
To assemble, place one cake layer on a plate and spread the lemon mascarpone filling on top. Add the second layer, cover it with the remaining filling, and press the crumb topping onto the cake. Dust with powdered sugar and refrigerate for at least 1 hour before serving.
Notes
Serve with extra mascarpone cream or fresh berries. Store in an airtight container in the refrigerator for up to 3 days.