Place the gluten free flour, salt, and pepper into a resealable plastic bag; shake to mix. Place the pheasant pieces into the flour mixture, and shake until evenly coated.

Heat the olive oil in a large skillet over medium-high heat.

Shake any excess flour off of the pheasant pieces, and place them in the hot oil.

Cook until the pheasant is brown on both sides, about 3 minutes per side.

Place the pheasant on a plate, reserving the oil in the skillet. Add more oil if necessary.

Cook the onion in the remaining oil until they soften, about 3 minutes. Stir in the mushrooms, artichoke hearts and garlic, and continue cooking and stirring until the mushrooms have softened and the garlic has mellowed, about 5 minutes more.

Pour the wine into the skillet and bring to a boil.

Boil for 5 minutes, then pour in the chicken broth and return to a boil, and sprinkle with sliced black olives.

Put the pheasant pieces back into the skillet, and continue cooking until the pheasant is cooked through, about 15 minutes.

Place pheasant with mushrooms, olives and artichokes on plates and serve.