In a large bowl, whisk together pomegranate molasses, olive oil, ground ginger, and ground fennel; season with salt and pepper.
In a large nonstick skillet, heat vegetable oil over medium-high heat. Season scallops with salt and pepper. When the oil is very hot, add as many scallops as will fit in a single layer, with at least 1/2 inch of space between them, and cook without turning until golden brown, 2 to 3 minutes. Turn scallops over and cook 1 1/2 to 2 minutes or until centers are slightly translucent. Repeat with remaining scallops.
Whisk dressing to combine. Add fennel, arugula, parsley leaves, and chives. Toss well. Add avocado and toss again. Taste and adjust seasonings if necessary.
To serve, put the salad in the center of a platter and arrange scallops on top. If desired, garnish with pomegranate seeds.