Preheat the oven to 350 degrees F. Line the bottom of three 6-inch round cake pans or two 8-inch round cake pans with parchment paper rounds. Spray the parchment paper and sides of the pans with nonstick cooking spray. This step is crucial; you really must use parchment paper or the cakes will stick to the pan, ruining your beautiful creation.
Prepare the pistachios: Add 1 cup of pistachios to the bowl of a food processor and process on high until they are finely ground, about 30 seconds to 1 minute. Be sure to reserve 1 to 2 tablespoons of ground pistachios to decorate the cake later.
Mix the dry ingredients: In a large bowl, add the ground pistachios (minus the reserved portion), then whisk in the almond flour, oat flour, baking powder, baking soda, and kosher salt. This mixture will form the foundation of your cake.
Combine the wet ingredients: In a separate large bowl, add the granulated sugar and lemon zest. Use your clean fingers to rub the zest into the sugar for about 1 minute. This infuses the sugar with the bright lemon flavor. Then add the eggs, Greek yogurt, lemon juice, and almond extract; whisk until everything is smooth and well combined.
Incorporate the dry into the wet: Add the dry ingredients to the wet ingredients and mix gently with a wooden spoon until the batter is smooth. If you want to add a fun twist, mix in 1 to 2 drops of dye-free food coloring to give the cake a more vibrant color.
Divide the batter: Carefully divide the batter evenly between the prepared pans. Use a spatula to spread it out and smooth the tops, ensuring even baking.
Bake the cakes: Place the pans in the oven and bake for 18 to 25 minutes for the two 8-inch pans, or 22 to 28 minutes for three 6-inch pans. The cakes are done when a tester comes out clean or with just a few crumbs attached. Allow them to cool completely in the pans.
Frost the cake: Once the cakes are completely cool, it’s time to assemble! Place about 1 to 2 tablespoons of frosting on your cake stand to hold the cake in place. Invert one of the cakes, flat side up, and add about ½ heaping cup of frosting, spreading it toward the edges. If using strawberry jam, add 3 tablespoons on top of the frosting and spread it out, leaving about a ¼ inch border. Repeat this with the next layer.
Crumb coat the cake: After layering, frost the top and sides of the cake with a thin layer of frosting. Use a bench scraper or offset spatula to create a smooth finish. This is called a crumb coat and allows for a beautiful finish once you frost it again.
Chill the cake: Transfer the cake to the fridge for 15 to 20 minutes until the crumb coat is firm to the touch. Once chilled, repeat the frosting process with the remaining frosting until smooth. If your cake looks slightly ‘naked’ on the outside, that’s perfectly fine—it’s going to be delicious!
Garnish and serve: Before serving, dust the top with reserved ground pistachios and decorate with fresh strawberries or other berries of your choice to make it visually stunning. Enjoy immediately or store the cake in the fridge for up to 5 days in a well-covered container.