Step 1

For the cake: Preheat the oven to 350 degrees F. Grease a Bundt pan.

Step 2

Whisk together the flour, pudding mix, baking soda and salt in a medium bowl. Set aside.

Step 3

Beat the butter, oil and granulated sugar in the bowl of a stand mixer fitted with the paddle attachment at medium-high speed, scraping down the sides of the bowl as needed, until pale and fluffy, 4 to 6 minutes. Reduce the speed to low and add the eggs, one at a time, beating until the yellow disappears after each addition. Beat in the vanilla extract, lemon zest and lemon juice just until combined.

Step 4

Beat in the flour mixture alternately with the milk in 3 additions, beginning and ending with the flour mixture. Beat just until the ingredients are combined.

Step 5

Scrape the batter evenly into the prepared Bundt pan and bake until the cake is golden brown and a toothpick inserted in the center comes out mostly clean with only a couple of moist crumbs, 1 hour 5 minutes to 1 hour 10 minutes. Let the cake cool in the pan for 15 minutes. Run a knife around the edges of the cake and invert onto a cooling rack to cool completely, about 45 minutes.

Step 6

Meanwhile, make the lemon drizzle: Whisk together the confectioners' sugar, lemon juice and vanilla until thick. (If it’s too runny, add a little more confectioners' sugar.) After the cake is cooled, pour the lemon drizzle over the top.