Preheat oven to 350°F (180°C). Grease sides of a 9-in. (23 cm) round springform pan and line bottom with parchment paper cut to size. In a small bowl, mix graham crumbs and butter. Press evenly onto bottom of pan to create crust. Bake until golden brown, about 10 min. Let cool completely.
Meanwhile, using an electric mixer (stand or hand-held), beat together cream cheese, 1/2 cup (125 mL) sugar, sour cream, eggs and fresh ginger until fully incorporated. Pour batter into pan and spread evenly. Bake until centre is just set, with a slight jiggle, about 40 min. Cool completely to room temperature before refrigerating overnight to set.
Once set, make a glaze by bringing 1/2 cup (125 mL) sugar and orange juice to boil in a medium saucepan over medium-high heat. Lower heat and simmer until liquid reduces to 1/2 cup (125 mL), about 20 min. While liquid is simmering, soak candied ginger in hot water for 10 min. then finely dice. Stir in candied ginger once liquid is reduced.
Preheat oven to broil. Peel and remove pith from navel oranges, then cut into segments. Spread in a single layer on a parchment paper–lined baking sheet and sprinkle 2 tsp (10 mL) sugar overtop. Broil until golden and slightly caramelized, about 5 to 7 min. Garnish cake with bruléed orange slices and drizzle glaze overtop.
Bake this cheesecake a day ahead to allow time for it to set in the refrigerator.