Step 1 Drain the canned mandarin oranges, reserving the juice; you should have 1 1/2 cups reserved juice (if you are short, make up the difference with additional orange juice).
Step 2 In a large, heavy-bottom saucepan, combine the canned oranges, reserved mandarin juice, 2 1/2 cups orange juice, ginger and sugar over high heat.
Step 3Bring the mixture to a strong simmer and cook, stirring frequently, until the compote is reduced to sauce consistency, about 40 minutes. As the compote reduces, the color will deepen to a rich apricot shade.
Step 4When the compote is almost reduced, in a small bowl combine the remaining one-fourth cup orange juice with the cornstarch, whisking to thoroughly combine and form a slurry.
Step 5Add the slurry into the reduced compote, stirring until the compote thickens, about 1 minute. Remove from heat. This makes about 1 1/2 cups compote. You might not use all of the compote for the remainder of the recipe; to store, cool the compote then cover and refrigerate until needed. The compote will keep for about a week, refrigerated. Gently warm in a saucepan before serving.