1Preheat oven to 400°F. Prepare 4 pieces of parchment paper or foil for papillotes (see Tip).
2Remove skin and white pith from the oranges, using a sharp knife. Cut the segments away from their surrounding membranes. Squeeze any remaining juice from the membranes into a small bowl. Stir in orange juice concentrate, thyme, soy sauce, garlic and pepper.
3Open the papillotes and place a piece of tuna on one half of each opened paper heart. Distribute mushrooms and orange sections over the tuna. Spoon orange juice mixture over top. Seal the packages and place them on a baking sheet. Bake until the packages have puffed, 10 to 12 minutes. (You may want to open one package to check that the tuna flesh is opaque.) Transfer the packages to individual plates; let each diner open his or her own package.
To prepare a papillote: Cut a piece of parchment paper or foil about 12 inches by 16 inches. Fold in half an 8-by-12-inch rectangle, then cut into a half-heart shape as you would a Valentine.
People with celiac disease or gluten-sensitivity should use soy sauces that are labeled "gluten-free," as soy sauce may contain wheat or other gluten-containing sweeteners and flavors.