Cut two, 6-inch squares of waxed paper or parchment and place on your serving plates. Place the presentation ring or biscuit cutter in the center of the waxed paper and set aside. (If you only have one ring or cutter, you will need to prepare each Napoleon separately.)
Working inside the presentation ring or biscuit cutter, begin the base layer of beets. Scatter and press in gently so as to fill all edges and gaps, the base layer of beets. You may need to use a small spoon to get the pieces where you want them - it's a process. Build your base layer to about 1/2 to 3/4 inches tall.
Using a clean small spoon, drop half of the goat cheese in small dollops atop the base layer of beets, filling all of the gaps and spaces. Using the back of that spoon or your fingers, gently press the goat cheese into the base layer. Do not pack the cheese down hard, rather press down but do so loosely. Only the outside of this cheese layer will be seen once assembled, so there's no need to smooth it out.
Follow with the last layer of beets, again being sure to fill fill all edges and gaps. Again, only the outside of this beet layer will be seen once assembled so do not be concerned that the pieces are uneven on the top.
Gently pull the waxed paper from beneath the Napoleon. Discard the waxed paper.
Once both Napoleons are assembled, add 1 tablespoon of the vinaigrette to the top of each, allowing the dressing to spill down and fill and flavor any interior nooks and crannies.
Highlight the top with beautiful frisée or mâche leaves and additional vinaigrette spooned over the greens and drizzled down the sides of the Napoleon. Serve with soft warmed yeast rolls and softened assorted compound butters.