Preheat & Prep: Set your oven to 350°F. Grease an 8-inch baking dish.
Melt Butter: In a small saucepan, melt the butter over medium heat. Once melted, remove from heat and let it cool.
Prepare Lemon Mixture: Zest both lemons into a large bowl, ensuring you get about 2 tablespoons. Add the granulated sugar and rub them together to infuse the sugar with lemon flavor.
Whisk the Eggs: Crack the eggs into the bowl and whisk vigorously for about 2 minutes. This helps create a light and fluffy texture.
Combine Wet Ingredients: Stir in the melted butter and vanilla extract, then fold in the crème fraîche until well blended.
Mix the Dry Ingredients: Without mixing yet, pile the flour on top of the wet mixture. Add the baking powder, baking soda, salt, and lemon pudding mix on top of the flour, then use your fingers to gently sift the dry ingredients together before incorporating them into the wet ingredients. Stir until just combined—avoid overmixing.
Bake: Pour the batter into the greased baking dish, smoothing the top. Bake for 40-50 minutes, or until the top turns golden and a toothpick inserted in the center comes out clean. Let the cake cool completely before frosting.
Make the Frosting: In a large bowl, use a spatula to soften the butter. Gradually add the crème fraîche, mixing until smooth. Slowly add the powdered sugar, one cup at a time, sifting to prevent lumps. Stir in the lemon juice, vanilla, and salt, then mix until the frosting is light and creamy.
Frost & Serve: Spread the frosting over the cooled cake, slice into 9 squares, and enjoy!