Heat oven to 350° F. Spread the pecans on a rimmed baking sheet and toast, tossing occasionally, until fragrant, 6 to 8 minutes. Let cool, and then roughly chop.
Combine the pecans, tarragon, lemon juice, 2 tablespoons of the oil, and ¼ teaspoon each salt and pepper in a small bowl; set aside.
Meanwhile, steam the potatoes and cauliflower in ½ inch of water in a large pot, covered, until very tender, 18 to 22 minutes.
Transfer the potatoes, cauliflower, 1 teaspoon salt, and ½ teaspoon pepper to a food processor and puree until very smooth.
Heat the remaining 2 tablespoons of oil in a large nonstick skillet over medium-high heat. Add the fish and cook until opaque throughout, 2 to 3 minutes per side.
Serve the fish over the cauliflower puree, topped with the tarragon sauce.