1. Make the sauce: Combine the carrot juice, honey, lemon juice, lime juice, tamarind paste, and salt in a small saucepan and place over medium-high heat. Bring to a boil for 30 seconds to dissolve the honey and tamarind. Stir in the rosemary; remove from the heat and cover. Let stand for 10 minutes to infuse the rosemary flavor into the sauce. Pour the sauce through a fine-mesh strainer into a blender.
2. Blend on low speed until smooth. While the motor is running, pour in the grapeseed oil in a slow steady stream until emulsified.
3. Lay the scallops side by side on several layers of paper towels to drain any excess natural liquid; make sure both sides are completely dry, as wet scallops do not cook well. Brush both sides of the scallops lightly with mayonnaise and sprinkle with salt—the mayonnaise prevents the scallops from sticking to the grill and helps the salt stick.
4. Preheat a charcoal or gas grill to high heat (500°F)
5. Put the scallops on the hot grill for 2 minutes, carefully turn them over, and grill the other side until they have a nice char, about 1 minute. Scallops are a little delicate; if one seems to stick, don’t try to pull it up, or you risk tearing it. Give it another 30 seconds and then try again.
6. To serve, drizzle the carrot sauce on a serving platter and arrange the scallops on top. Garnish with nasturtium leaves and flowers, if using.