Preheat oven to 340°F or 170°C. Line the bottom of your pan with parchment paper and brush sides with butter.
To a large mixing bowl, add the dry ingredients: 1½ cup all-purpose flour, 1 cup sugar, 1½ teaspoon baking powder, and ¼ teaspoon salt. Whisk to combine.
To a second bowl, add wet ingredients: the grated zest of 1 lemon, ¼ cup lemon juice, ¾ cup water, ¼ cup olive oil, 1 tablespoon vanilla extract, and 2 teaspoons lemon extract. Whisk to combine.
Pour wet ingredients into dry ingredients and whisk until just combined, without overmixing.
Transfer cake batter to your prepared baking pan.
Bake at 340°F or 170°C for 35 minutes or until a toothpick inserted in the center comes out mostly dry.Let cake cool down 10 minutes in the pan, then take it out and let cool down completely on a wire rack lined with parchment paper.
Spread frosting on top, keep in the fridge if not eating it immediately.Cut into slices, then you can add grated lemon zest on top before eating.
For the frosting
Soften 2 ounces vegan butter at room temp for 15 minutes, then add it to a mixing bowl with 1 teaspoon vanilla extract and the grated zest of ½ lemon. Beat with a hand mixer for 30 seconds.
Add 4 ounces vegan cream cheese and beat for 30 more seconds.Add 1 cup powdered sugar, beat on low speed first, scrape down sides, and finish beating on medium-high speed until perfectly smooth. Don't overbeat it.Let it firm up in the fridge for 30 minutes, or in the freezer for 15 minutes, before applying it on the cake.
Spread frosting on top of the cake, then let cool down 1 hour in the fridge or 15 minutes in the freezer before slicing and serving.