Special equipment: a pastry bag fitted with a 3/8-inch plain round tip (number 804); a pastry bag fitted with a 1/4-inch plain round tip (number 803)
For the cake: Position the oven racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Grease the bottoms and sides of two 8-inch round cake pans.
Prepare the cake batter according to the package instructions. Divide the batter evenly between the prepared pans. Bake the cakes, rotating the pans halfway through, until a toothpick inserted in the center comes out clean, 23 to 28 minutes. Let cool in the pans about 10 minutes, then turn out onto cooling racks and let cool completely.
For the frosting: Meanwhile, combine the butter, confectioners' sugar, vanilla, salt and 3 tablespoons milk the in the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a handheld electric mixer). Mix on low speed until mostly incorporated. Increase the speed to medium-high and mix until smooth, adding more milk as necessary to make a spreadable frosting.
Transfer 1 cup of the frosting to a small bowl and tint with the brown gel food coloring. Scrape the brown frosting into a pastry bag fitted with a 3/8-inch plain round tip (number 804).
Tint the remaining frosting with the lemon yellow and golden yellow gel food coloring. Fill a pastry bag fitted with a 1/4-inch plain round tip (number 803) with 3 cups of the yellow frosting.
Cover the remaining yellow frosting (about 3 1/4 cups) with plastic warp and reserve for frosting the cake.
To assemble: Place one cake layer upside down on an extra-large cutting board or platter (at least 20-by-14-inches). Using a serrated knife, cut the other cake layer into 8 wedges. Lightly trim the rounded side of each wedge so it is flat; discard the trimmings. Arrange the wedges around the cake, trimmed side against the cake, to create a sunflower shape.
Pipe a circle of yellow frosting around the center cake to create a 1/2-inch border.
Spread the reserved yellow frosting in the bowl evenly over the top and sides of the cake, (including the petals), leaving the circle inside the piped border unfrosted.
Pipe a continuous spiral of brown frosting inside the 1/2-inch yellow border, starting at the edge of the border and working in towards the middle until the center of the cake is filled.
Place one brown candy on its edge in the center of the brown frosting. Place a second candy next to it, leaving a candy-size space between. Continue to place candies around the center, working out towards the edge and arranging the successive rows of candies in the spaces between the previous rows until the center of the cake is filled.
Holding the pastry bag with the remaining yellow frosting at a 45-degree angle, pipe a small dollop of frosting on the edge of one of the cake petals, stopping and pulling the bag off the dollop to create a tip. Repeat the dollops, working out toward the tip of the petal until the petal is filled. Repeat with the remaining petals. Slice the cake and serve.
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