For the broth: Heat the oil in a medium saucepan over medium heat. Add the bacon and cook until golden brown and crispy, stirring occasionally, about 7 minutes. Remove the bacon and reserve for the relish.
Increase the heat to high, add the onions, celery, and carrots and cook until slightly soft, about 5 minutes. Stir in the garlic and cook 30 seconds. Add the wine and cook until almost completely reduced, and then add the fish stock and bring to a boil. Add the tomato puree to the broth and bring back to a boil. Cook until slightly reduced and thickened, about 10 minutes.
For the potatoes: Preheat the oven to 400 degrees F.
Place the potatoes on a baking sheet, toss with 2 tablespoons of the oil and season with salt and pepper. Roast in the oven until golden brown and just cooked through, turning once, about 15 minutes.
For the fish: Heat the oil in a large nonstick, oven-safe pan until it shimmers. Season the fish on both sides with salt and pepper and cook until golden brown. Turn over, transfer to the oven, and cook until just cooked through, 8 minutes. Cut crosswise into 4 equal pieces.
For the relish: Heat the oil in a small saute pan over medium heat. Add the reserved bacon and cook until golden brown. Add the garlic and red chile flakes and cook for 30 seconds. Stir in the parsley and transfer to a small bowl.
To serve: Ladle the broth into 4 bowls. Place a piece of halibut in the center of the bowl. Arrange 3 potato halves around the fish and garnish with the bacon relish.