Preheat an oven to 350 F. Grease and line an 8x8 metal baking pan with parchment paper so that there’s overhand over two sides. This makes extracting the cake from the pan much easier.
Mix the dry ingredients. In a small mixing bowl, whisk together the flour, baking powder, baking soda, and salt together and set aside.
Mix the wet ingredients. In a measuring cup, whisk together the buttermilk, sour cream, oil, and vanilla bean paste and set aside.
Beat the butter and sugar together. Combine the sugar and lemon zest in a large mixing bowl. Use your fingers to rub the lemon zest into the sugar until it’s very fragrant. Add the butter and use a hand mixer to cream the butter and sugar together until it’s very fluffy, about 3-4 minutes. Beat the eggs in, one at a time, until smooth. Add the yellow food coloring here if you’re using it.
Alternate in the wet and dry ingredients. Alternate between adding the dry and wet ingredients. Mix in 1/3 of the flour mixture, then half of the buttermilk mixture. Add another 1/3 of the dry ingredients and then the rest of the liquid ingredients. Switch to a rubber spatula and fold in the remaining 1/3 of the flour mixture until the batter is smooth and no streaks of flour remain.
Spread the batter in the pan and bake. Use a small offset spatula to evenly spread the batter into the prepared cake pan. Bake for 30-40 minutes, just until a cake tester comes out coated with a few moist crumbs. Remove the cake from the oven and let it cool for 30 minutes before inverting it onto a serving plate. Leave the parchment paper in place on the cake until the cake has cooled completely.
Make the frosting. In a mixing bowl, combine the softened butter, vanilla, and cream cheese and use a hand mixer to beat them together for 2 minutes, until smooth. Gradually beat in the powdered sugar, adding cream as necessary when the mixture gets too thick. Whip the frosting until it’s smooth and spreadable. Remove the parchment paper from the cooled cake and spread the frosting evenly all over the cake.