Grilled Strip Steak and Caesar Salad

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Dressing:

1/2 cup 2 percent plain Greek yogurt

3 tablespoons grated Parmesan

1 tablespoon plus 1 teaspoon fresh lemon juice 

1 tablespoon Dijon mustard

1 tablespoon olive oil

1/2 teaspoon dried oregano

3 anchovies

1 small clove garlic, chopped

Kosher salt and freshly ground black pepper

Steak and Romaine:

1 tablespoon olive oil, plus more for oiling the grill grates and brushing the romaine

Two 1-inch-thick strip steaks (about 1 1/2 pounds total), trimmed of excess fat

Kosher salt and freshly ground black pepper 

2 romaine hearts, split lengthwise and core trimmed