For the lemon and olive oil cake: Preheat oven to 350°F (180°C). Grease a 9 x 5-in (23 x 12 cm) loaf pan, then line with a sling of parchment paper. (This will make it easier to unmold the lemon and olive oil cake later on.)
In a small bowl, combine the sugar with the lemon zest. Using the back of a spoon, rub the zest into the sugar for about 2 minutes, or until the sugar is moist and aromatic. (This step will produce a stronger, more aromatic lemon flavor in the cake.)
Transfer the lemon sugar to the bowl of a stand mixer fitted with the paddle attachment, or to a large mixing bowl if using a hand mixer. Add the eggs and beat at medium-high speed for at least 4 minutes, or until the batter has doubled in volume, looks creamy and light, and is of a very pale yellow color.
In a small bowl, whisk the flour and baking powder together, then add to the egg and sugar mixture. Mix in at low speed just until combined. Add the olive oil, honey, melted butter, and lemon juice, and mix at low speed to combine.
Transfer the batter to the prepared loaf pan. Bake for about 60 minutes, until a toothpick inserted in the middle of the cake comes out clean.
While the cake is baking, make the lemon syrup: In a small saucepan, whisk the lemon juice and sugar together. Set over medium-low heat and whisk just until the sugar is fully dissolved. (You can also prepare the syrup in the microwave.) Set aside.
Transfer the hot cake in its pan to a wire rack. Using a toothpick, poke holes all over the top of the cake. Using a pastry brush, slowly brush the lemon syrup all over the cake, letting the cake absorb the syrup before adding more. Repeat until all the syrup is used. Let the cake cool completely.
At this stage, you can freeze the lemon and olive oil cake: unmold and wrap the cake tightly in plastic wrap, store in an airtight container or in a heavy-duty freezer bag and freeze for up to 2 months.
On the day you plan to serve the cake (or up to 2 days ahead of serving time), make the one-step Italian meringue: In a clean, stainless steel bowl, combine the egg whites, sugar, water, and cream of tartar. In a saucepan slightly smaller than the stainless steel bowl, pour an inch of water, then set over medium heat to bring to a simmer. Set the stainless steel bowl over the simmering water, making sure the bottom of the bowl does not touch the water directly, and beat the meringue with a hand mixer on low speed for 4 minutes. Increase the speed to high and beat until the meringue is bright white and thick, 4 minutes more. Remove the bowl from the heat and keep beating until the meringue is fluffy and room temperature to the touch, 4 to 6 minutes more.
If making the Italian ahead of time, transfer it to an airtight container and refrigerate until needed.
SERVING: Bring the lemon and olive oil cake back to room temperature at least 1 hour before service. If the Italian meringue was made ahead of time, give it a good whisk to loosen it. Set the lemon and olive oil cake on a serving plate. Pile the Italian meringue on top of the lemon and olive oil cake. Use a kitchen torch to toast the meringue all over. Serve the cake cut into thick slices, along with fresh berries, if desired.
STORAGE: Store leftover lemon and olive oil cake under a cake dome or in an airtight container at room temperature for up to 2 days, or in the fridge for up to 4 days.
Recipe Credits: Cake recipe adapted from Alba Pezone, one-step Italian meringue recipe adapted from David Joachim’s Brilliant Food Tips & Cooking Tricks.