Grilled Plum and Pistachio Salad

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4 plums, pitted, halved and each half cut in 3

2 tablespoons olive oil, divided 

1/2 teaspoon kosher salt, divided 

1 head bibb lettuce, torn into bite-sized pieces 

1/4 cup chopped fresh basil leaves 

1/4 cup chopped fresh mint leaves 

1 tablespoon white balsamic vinegar 

1/4 cup toasted pistachios, chopped 

1/2 cup ricotta salata cheese shavings