Creamy Tomato Gazpacho With Crunchy Pecorino

Name: Creamy Tomato Gazpacho With Crunchy Pecorino
Ingredients: 6 tablespoons grated pecorino Romano; 2 large tomatoes (about 1 pound), cored and roughly chopped; 1 1/2 cups (12 ounces) plain sheep’s-milk or regular yogurt; 1/4 cup extra virgin olive oil, more for serving; 12 basil leaves, roughly chopped, more for serving; 2 large garlic cloves, peeled and roughly chopped; 2 scallions (white and light green parts), roughly chopped; 2 ice cubes; 1 3/4 teaspoons kosher salt, more to taste; 1 1/2 teaspoons red wine vinegar, more to taste; Pinch cayenne pepper; Ground black pepper to taste