Heat the oven to 425 degrees.
Place the shrimp, 3/4 teaspoon kosher salt, 1/2 teaspoon oregano, lemon zest and 2 tablespoons olive oil into a bowl. Stir well. Set aside.
Place the tomatoes and 1 onion into a bowl. Toss with 1 teaspoon kosher salt, 2 tablespoons olive oil and 1/2 teaspoon oregano. Pour the mixture onto a rimmed baking sheet. Place into the oven and roast for 35-40 minutes. To achieve a char on the vegetables, broil the mixture for the last 3-5 minutes of roasting.
Remove the vegetable mixture from the oven. Carefully pour the juices into a small bowl. Add 1/3 cup olive oil to the pan juices. Stir to combine and let cool for 10 minutes. Place the shrimp in one layer onto the sheet pan. Place back into the oven and cook for 8-10 minutes, or until the shrimp is pink and cooked through. Remove the sheet pan from the oven and let the shrimp cool for 10 minutes.
Meanwhile In a small bowl combine the lemon juice, vinegar, mint and a pinch of salt. In a steady stream add the pan juices to the mixture, whisking continually.
Place the lettuce, sliced red onions, cucumbers, cheese and olives into a large serving bowl. Toss the salad with the vinaigrette (to taste) and shrimp. Serve immediately or chilled.