Preheat oven to 400°F. Fill medium saucepan with water and bring to a boil. Add beet noodles and boil 1 minute. Place beets in colander and run under cool water to remove excess color. Drain beets and blot well on paper towels.
On remaining tart area, arrange beet noodles in 4 rows about 1-1/2 inches wide each, leaving about 1-inch between rows. Carefully place crumbled goat cheese between beet spiral rows.