Preheat the oven to 320 F (160 C). Line the bottom of an 8-inch (20 cm) tall cake pan or springform pan with parchment paper. Butter and flour the sides of the pan.
In a bowl, whisk together the flour, baking powder, and salt.
In a stand mixer fitted with the paddle attachment, or using a hand mixer and bowl, cream together the sugar, butter, and vanilla extract until light and fluffy.
Add the vegetable oil and mix until incorporated.
Add the egg and beat again.
Add the mascarpone cheese and mix until fully combined, then add the milk and mix to combine.
Add the dry ingredients and mix on low speed until just incorporated. The batter should be thick.
Spread the batter evenly into the prepared pan and bake for about 45 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan until safe to handle. Remove from the pan and wrap in plastic wrap. Refrigerate until completely cooled.