Scrub the beets and place the golden beets and the chioggia or red beets in separate saucepans. Cover with water by about an inch. Bring water to a boil on high heat, then reduce heat and simmer for about 45 minutes, until beets are soft when pierced with a fork. Remove, drain, cool the beets and then trim and peel. Slice into 1/2 inch slices. Set aside.
Zest the oranges and reserve about 2 tablespoons of zest. Juice the oranges and strain the juice. Put the juice in a saucepan and bring to a boil over high heat. Reduce heat to lowest setting and simmer until the juice is reduced to about 1/4 cup and is syrupy.
Crumble the chèvre into a bowl. Add the orange zest and mix well. Roll the cheese into a log, wrap in plastic wrap and chill for about 10 minutes. Remove the cheese and slice into disks. Dip the disks into the egg wash and then roll them in the ground sesame stick crumbs.
Heat the oil in a non-stick pan over medium heat. Brown the chèvre disks on both sides and remove to a plate.
To assemble, spread the orange reduction onto a plate and arrange the sliced beets on top. Arrange the chèvre over the beets and scatter the fennel on top.