Crunchy Baked Chicken With Ham and Swiss

Name: Crunchy Baked Chicken With Ham and Swiss
Ingredients: 2 tablespoons olive oil, divided; 2 pounds chicken breast cutlets (about 8 cutlets); 1 ½ teaspoons kosher salt, divided; ½ teaspoon freshly ground black pepper; 2 cups whole milk, divided; 1 tablespoon chopped fresh thyme; 2 tablespoons all-purpose flour; 3 ounces Swiss cheese, coarsely grated (about ¾ cup); 2 ounces thinly sliced prosciutto, torn into 1-in. pieces; ⅓ cup panko; 12 ounces haricots verts or green beans, trimmed