Season the monkfish with salt and pepper to taste.
Heat 2 tablespoons of the olive oil in a large cast-iron casserole cooker. Add the fish to the casserole over moderate heat, turn the fish, until light golden (3 minutes). Transfer the monkfish to a plate using a slotted spoon.
Cook the shallots in the casserole for approximately 2 minutes or until softened. Stir occasionally.
Add the carrots and cook for 5 more minutes, while stirring. Add the thyme, saffron and wine. Cook for 1 minute until reduced by half.
Add 1 cup of water along with the monkfish. Bring just to a simmer, cover and cook over low heat until the vegetables are tender and the fish is cooked through (15 minutes).
Spoon the stew into shallow bowls. Garnish with basil and serve with mashed potatoes!