In a small bowl, reconstitute dried mushrooms in water according to package instructions. Drain, and reserve the water. Chop reconstituted mushrooms into small pieces.
Heat olive oil in a large heavy skillet over medium heat. Saute pheasant meat with garlic and basil until lightly browned. Remove meat from pan with a slotted spoon, and set aside. Add butter to oil in skillet. Saute shallots, reconstituted mushrooms and portobello mushroom until golden brown. Stir in sun-dried tomatoes, and all but 1/4 cup of the mushroom soaking water. Dissolve arrowroot powder in water, and stir into mushroom mixture. Return pheasant meat to skillet, and simmer 30 minutes.