6 (4-to 5-ounces) mackerel fillets with skin, halved
1/3 cup plus 2 tablespoons extra-virgin olive oil, divided
2 tablespoons fresh lemon juice
1 tablespoon Dijon mustard
1 medium head radicchio (about 10 ounces), leaves torn
2 tablespoons chopped flat-leaf parsley
Make several diagonal slashes (1/8 inch deep) in mackerel skin about 1 inch apart.
Coat both sides of mackerel with 2 tablespoons oil, then season with 3/4 teaspoon salt (total).
Broil mackerel, skin side up, in a 4-sided sheet pan about 4 inches from heat until just cooked through and skin is crisp in spots, about 7 minutes.
Meanwhile, whisk together remaining 1/3 cup oil, lemon juice, mustard, 1/4 teaspoon salt, and 1/8 teaspoon pepper in a large bowl.
Reserve 2 tablespoons vinaigrette, then toss radicchio and parsley with remaining vinaigrette.
Serve salad topped with avocado and mackerel and drizzled with reserved vinaigrette.