In a small bowl, sprinkle gelatin over 1/4 cup cream. Let stand, without stirring, until gelatin is soft, about 10 minutes.
Meanwhile, pour remaining 1 3/4 cups cream into a 1- to 2-quart pan over medium heat. Scrape seeds from vanilla bean into cream, then add the bean (if using vanilla extract, add after yogurt, below), sugar, and orange peel; stir until sugar is dissolved and mixture is simmering. Remove from heat. Add gelatin mixture and stir until gelatin is completely dissolved. Pour into a large bowl. Remove vanilla bean and orange peel and let cool 10 minutes. Add yogurt (and vanilla extract, if using) and stir until well blended.
Lightly brush a 4-cup tube mold (or eight 1/2-cup molds) with oil; pour cream mixture into mold. Cover and chill until set, 8 hours or up to 2 days.
Just before serving, unmold: Gently run a knife between panna cotta and sides of mold to loosen. Invert a plate over mold and, holding plate and mold together, turn over; lift off mold. If panna cotta doesn't slip out easily, immerse mold to just below rim in warm water for about 2 seconds; lift out, dry bottom of mold, and repeat to invert onto plate.