Line up three medium bowls on the counter. Whisk the flour, 2 tsp. salt, and 1 tsp. pepper in the first; lightly beat the eggs in the second; and mix the almonds, lemon zest, and 1/2 tsp. salt in the third. Lightly season both sides of the fish with salt and pepper. Dredge each piece in the flour, then the egg, and then the almond mixture, pressing the nuts onto the fish so they adhere.
Heat 2 Tbs. of the oil in a 12-inch skillet over medium heat. Add the fish and cook, flipping once, until browned on both sides and flaky throughout (cut into a piece to check), about 4 minutes per side.
Meanwhile, put the greens in a large bowl. In a small bowl, whisk the lemon juice, shallot, tarragon, 1/2 tsp. salt, and 1/4 tsp. pepper. Gradually whisk in the remaining 1/2 cup olive oil. Toss the greens with enough of the vinaigrette to lightly coat. Season to taste with salt.
Divide the greens among 4 plates and top with one of the halibut fillets. Drizzle some of the remaining vinaigrette over each and serve.