Trim tops of okra, being careful not to cut into pods.
Cut an X in bottom of each tomato and immerse tomatoes in a 2-quart saucepan of boiling water for 10 seconds. Transfer tomatoes with a slotted spoon (save boiling water) to a bowl of ice and cold water to cool, then peel. Add 1 tablespoon salt to boiling water, then add okra and cook, uncovered, until just tender, about 5 minutes. Drain okra in a colander, then plunge into same ice water to stop cooking. Drain okra and pat dry with paper towels.
Quarter tomatoes lengthwise and seed, then cut each quarter lengthwise into 1/2-inch-wide strips.
Puree onion, garlic, ginger, jalapeno (to taste), and 1/4 cup chicken broth in a blender.
Pat scallops dry and sprinkle with pepper and remaining 1/2 teaspoon salt. Brush a 12-inch nonstick skillet with 1/2 teaspoon oil and heat over moderately high heat until just beginning to smoke. Brown scallops in 2 batches, turning once, about 4 minutes total. Transfer scallops as browned with tongs to a plate and keep warm, covered with foil. (Scallops will not be cooked through.)
Add remaining 1 1/2 teaspoons oil to skillet and reduce heat to moderate. Add puree carefully (it may splatter), then add curry powder. Boil, stirring constantly, 2 minutes. Add coconut milk and remaining 3/4 cup broth and bring to a simmer. Add tomato strips and simmer, stirring frequently, until tomatoes are softened, 3 to 4 minutes. Season sauce with salt and pepper.
Stir in scallops and okra and simmer until scallops are just cooked through, about 3 minutes. Divide scallops, vegetables, and sauce among 4 plates and sprinkle with cilantro.
Serving Suggestion: Spiced basmati rice .
Tomatoes can be peeled, seeded, and cut into strips 4 hours ahead, then kept, covered, at room temperature. Okra can be blanched and refreshed 4 hours ahead and chilled in a sealed plastic bag with a paper towel.