Put the olive oil in a Dutch oven over medium-high heat. When it is hot, sprinkle the fish with salt and pepper, and add it to the pot. Cook, undisturbed, until it is well browned, 5 or 6 minutes. (If you’re using halibut fillet, and it has skin, brown the nonskin side.) Transfer it to a plate, browned side up.

Add the onion, thyme, saffron, carrots, fennel and potatoes; sprinkle with salt and pepper. Cook, stirring occasionally until the onion begins to soften, about 5 minutes. Add the tomato paste and smoked paprika, and cook, stirring, until the tomato paste darkens a bit, 2 or 3 minutes. Add the wine, scraping up any browned bits from the bottom of the pot, and let it bubble away until it almost disappears.

Add the stock, bring to a boil and let it bubble vigorously until the liquid reduces by about a third, about 10 minutes. Adjust the heat so the mixture simmers; when the vegetables are nearly tender — about 10 minutes later — nestle the fish, browned side up, among the vegetables; keep the browned crust above the liquid. Cook, undisturbed, until the fish and vegetables are tender, 10 to 15 minutes.

Transfer the fish to a cutting board, and divide the vegetables among shallow bowls. Slice the fish and put it on top of the vegetables. Taste the cooking liquid, and adjust the seasoning; ladle it over all, garnish with the parsley and serve.