For cake: In a mixing bowl, combine flour, baking powder, baking soda and salt. Whisk together and set aside.
Place butter into another mixing bowl and beat using an electric hand mixer. Add granulated sugar and continue to beat together. Add eggs and continue to beat together.
In thirds, alternating between flour mixture and milk, add to wet mixture until fully combined and batter is smooth. Fold in vanilla extract and tangerine zest until just combined.
Pour mixture into lightly greased 9-by-13-inch baking pan. Bake cake for 35 to 38 minutes or until toothpick comes out clean when inserted into the center of the cake. Cool cake completely.
For buttercream: Place butter into a mixing bowl and beat together with hand mixer. Add powdered sugar, 1/2 cup at a time, to butter and beat together until all sugar has been added. Add heavy cream, vanilla extract and salt and continue to beat together until light and fluffy.
To assemble: Slice 1/2-inch-thick rings crosswise of tangerine and set aside. Slice each strawberry in half lengthwise. Lay each strawberry half, cut-side down, and create three small "v" cuts on top of each strawberry to create a 'tulip' shape. Set aside.
Flip cooled cake from baking pan onto a platter. Top cake with buttercream and spread in an even layer. Spread thyme and mint sprigs evenly over bottom two-thirds of cake. Place tangerine slices evenly over tops of thyme sprigs, spreading them out throughout the cake. Place strawberries over remaining thyme sprig tops. Place blackberries over the tops of each mint sprig. Sprinkle a small amount of poppy seeds into the center of each tangerine slice.