Season the monkfish medallions with 1/2 teaspoon thyme, salt and pepper.
In a small heavy skillet heat 1 tablespoon of the butter over moderate-high heat until the foam subsides and in it sauté the monkfish medallions, turning once, for 10 minutes or until cooked through. Remove from the heat and tent with foil to keep warm.
In the skillet add the remaining butter and cook the garlic over moderate-low heat, stirring, and add the tomato, lemon juice, and the remaining 1/4 teaspoon thyme and cook, stirring frequently, for 5 minutes. Add the red pepper flakes, if desired.
Stir in any juices that have accumulated around the medallions, the parsley, salt and pepper to taste.
Arrange the medallions on heated plates and spoon over the sauce.