To prepare the relish, combine all ingredients, from green tomatoes to the dried mustard, in a 2.5-qt. sauce pan and bring to a boil.
Reduce heat to a simmer and cook for 20 minutes. Cool relish and set aside.
To prepare the fish, preheat oven to 400°F/205°C.
Heat a 10-in. sauté pan over medium-high heat until the pan is hot to the touch. Add olive oil to pan and swirl to coat. Season fish filets with salt and pepper.
Add halibut, flesh side down, to the pan and sear until golden, about 3 minutes. Turn fish over with spatula and place the pan in a pre-heated oven for about 10 minutes or until halibut is just cooked through.
Remove roasted filets from the oven and spoon some green tomato relish evenly over each filet. Serve immediately.
Extra green tomato relish can be stored for two weeks in a refrigerator.