Bring 2 cups water and 1 cup sugar to boil in medium saucepan, stirring until sugar dissolves. Reduce heat to medium and simmer 5 minutes. Cool syrup. Stir in lime juice.
Transfer lime syrup to 11 x 7 x 2-inch glass baking dish. Cover and place in freezer. Stir every 45 minutes until frozen, about 3 hours. DO AHEAD Granita can be made 2 days ahead. Cover and keep frozen.
Place sugar on small shallow plate.
Brush both sides of 1 mint leaf lightly with egg white; dredge in sugar.
Transfer mint leaf to rack. Repeat with remaining mint leaves.
Let mint stand at room temperature until dry, about 3 hours. DO AHEAD Can be made 1 day ahead. Store in airtight container at room temperature.
Mix créme fraîche and sugar. DO AHEAD Can be made 1 day ahead. Cover and chill.
Using fork, scrape granita to loosen. Spoon granita into bowls or lime halves; drizzle with créme fraîche, garnish with candied mint leaves, and serve immediately.