Make the saffron vinaigrette. Whisk together the white wine vinegar with the garlic, dijon mustard, and pinch of saffron. Slowly add the olive oil, whisk continuously. Season the vinaigrette with salt and pepper and set aside.
Marinate the halibut. Combine 1 teaspoon garlic with paprika and olive oil. Season both sides of the fish with salt and pepper and rub the marinade into the fish. Let sit at room temperature for 20 minutes.
Cut the Yukon potatoes into medium-size chunks. Place in a large pot and cover with enough water to cover the potatoes. Season the water with salt, cover the pot, and bring to a boil. Reduce heat and continue to simmer until the potatoes are fork-tender, about 10 minutes. Drain.
Heat 1 tablespoon oil in a large saute pan over medium-high heat. Add the potatoes and arrange them in one even layer. Continue to cook the potatoes until browned, about 3-4 minutes. Season the potatoes with salt and pepper. Remove from heat and toss the potatoes with half of the dressing. Keep warm.
In the same pan, heat another tablespoon of oil. Add the chopped chorizo and cook until caramelized and browned. Remove from heat and set aside.
Heat another tablespoon of oil in the same pan. Cook the halibut until browned and the fish flakes easily. If the filets are thick, cover the pan to help cook the inside. Remove from heat.
Arrange the plate. Place the potatoes on the plates with the fish. Sprinkle the chorizo, green onions, and crumbled feta on top. Drizzle the remaining saffron vinaigrette and serve immediately.