Heat the oven to 375°F and grease a 2 1/2-quart baking dish.
Melt 2 tablespoons butter in a saucepan, whisk in the flour and cook for 1 minute.
Whisk in the warm milk and simmer until thick enough to coat a spoon, about 4 minutes, then add the mustard, salt, black pepper and 3/4 cup Parmesan.
Fold the sauce with the rice, cooked chicken and artichokes and spread it in the baking dish.
Mix the panko, remaining Parmesan and remaining melted butter and scatter the mixture on top.
Bake until the sauce bubbles and the top is golden, 25 to 30 minutes.