Set a fine-mesh sieve lined with three paper towels over a medium bowl. Place Chobani in sieve and strain overnight in refrigerator.
Stir together cherries, sugar, and 1/3 c water in a medium saucepan set over medium-high heat. Once the mixture comes to a simmer reduce heat to medium-low and cook until cherries are soft and juicy, about 10 minutes.
In a small bowl stir together remaining 2 T water and cornstarch. Stir into cherries and once the mixture returns to a boil and becomes thick and glossy, turn off heat and transfer cherries to a medium bowl. Cool 15 min and then scrape cherry mixture into piecrust and refrigerate for at least 3 hours.
Melt the white chocolate in a microwave-safe bowl, stirring every 15 seconds. Set aside to cool until no longer warm to touch, about 10 minutes, then whisk in strained Chobani. Refrigerate until completely cool, about 10 minutes. Whisk in whipped cream. Spread over cherry filling and chill 30 minutes before serving.