Heat a grill (or grill pan) to medium-high heat.
Wash any grit from the romaine hearts and pat dry with a paper towel.
Brush the olive oil on both sides of the romaine. Then sprinkle with the salt and black pepper.
Place the romaine hearts, cut side down on the grill. Cook for 3 minutes, then flip and sprinkle the parmesan cheese on top of the romaine hearts. Grill for an additional 2 minutes.
Remove the romaine from the grill and place on a large platter.
Place the yogurt, mint, dill, red wine vinegar, olive oil, sea salt, and pepper in a bowl and whisk to combine. Add a tablespoon or two of water to the dressing to thin it to the desired consistency.
Drizzle the dressing over the romaine hearts and serve immediately.