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In a blender or food processor, combine the mayonnaise, sour cream, milk, 1 tablespoon of the lime juice, the chives, parsley, half of the jalapeño, half of the garlic, and the olive oil, and paprika. Blend until incorporated. Season the ranch dressing to taste with salt and pepper.
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In a small bowl, combine the tomatoes, onion, and cilantro and the remaining jalapeño, and garlic, and 1 tablespoon lime juice. Stir to combine and season to taste with salt and pepper. Set the salsa aside at room temperature to marinate.
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Preheat a grill or stovetop grill pan to medium-high heat. Brush the cut edges of the romaine, the avocados, and limes with olive oil. Lightly oil the grill or grill pan, then grill the avocados and limes cut sides down. After 3 minutes, remove the limes from the grill and add the romaine, cut sides down. Grill the avocado and romaine for 2 minutes longer, then remove.
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Transfer the grilled romaine to a platter and drizzle with the jalapeño ranch dressing. Top with the salsa and serve each wedge with a grilled avocado half and a grilled lime wedge. Finish with a sprinkle of salt.