How to Make It
In a medium saucepan, mix the rhubarb, sugar, lemon juice, cinnamon and ground ginger and bring to a boil. Reduce the heat to low and simmer, stirring frequently, until the rhubarb is tender but not falling apart, about 8 minutes. Transfer the rhubarb to a small bowl and let cool. Cover and refrigerate until thick, at least 1 hour and up to 1 day.
In a saucepan, whisk the tapioca, milk, eggs, sugar and salt. Let stand for 5 minutes, or until the tapioca begins to swell.
Bring the tapioca to a boil over moderately high heat, whisking constantly. Reduce the heat to moderately low and cook, stirring constantly, until slightly thickened, about 1 minute. Remove from the heat and stir in the vanilla. Set the saucepan in a bowl of ice water and stir often until cool and thick, about 5 minutes. Stir in the crème fraîche.
Spoon 1/4 cup of the rhubarb compote into 4 parfait glasses and top with half of the tapioca. Repeat with the remaining compote and tapioca. Garnish each parfait with 2 slices of crystallized ginger and serve.