Preheat oven to 350˚F.
For cake: Place flour, baking powder, baking soda, and salt into a mixing bowl.
Place sugar, butter and eggs into another mixing bowl and whisk together. Pour the flour mixture into the egg mixture and whisk together until very thick and combined.
Stir in the remaining ingredients except for the zest and thyme, until fully incorporated and the batter is smooth.
Gently fold in the zest and thyme until just combined.
Pour the batter into two prepared cake pans (bottoms lined with parchment and lightly greased) and bake for 25 to 30 minutes or until a toothpick comes out clean when inserted into the center of the cake.
Allow the cakes to cool in the pans for 15 to 20 minutes before removing from pans and allowing to cool completely.
For frosting: Place butter into a stand mixer, with a paddle attachment, and whip until light and fluffy. Add sugar, 1/2 cup at a time, until fully incorporated and most of the lumps disappear. With the motor running, add the remaining ingredients and continue to whip until smooth. (the frosting should be on the thinner side…not firm enough to pipe, but not so runny that it can’t be spread onto the top and sides of the cake)
For candied lemon peels: Scrub lemons to get rid of outer waxy coating. Trim ends of each lemon, then run a knife around the remaining peel, so you are left with "sheets" of peel. Remove the white pith from each sheet. Using a pairing knife, cut out mini lemon shapes from each sheet.
Bring 2 cups water to a boil and add lemon shaped peels. Simmer for 30 minutes to soften. Using a slotted spoon, remove peel pieces. Add 1 1/2 cups sugar to water and bring to a boil until sugar dissolves. Lower heat to medium-low and simmer. Add lemon peels into simple syrup and simmer for 30 minutes.
Using a slotted spoon, strain candied lemon peels from liquid and toss with remaining cup sugar. Line candied lemon peels onto a piece of wax paper. Top with another piece of wax paper and weigh down with a baking sheet, about 30 minutes (this will prevent the pieces from curling). Remove baking sheet and top layer of wax paper and allow pieces to dry completely.
To assemble and decorate: Spread frosting over the top of one cake and stack other cake on top. Frost the top and sides of the cake. Arrange candied lemons around the top of the cake and finish the tops of each mini lemon with two thyme leaves.