Green Goddess Whipped Feta Dip

Name: Green Goddess Whipped Feta Dip
Ingredients: 8 ounces feta; 1 cup (or more) buttermilk; 2 cups cilantro leaves with tender stems; 2 cups parsley leaves with tender stems, plus sprigs for serving; ½ cup tarragon leaves; 4 oil-packed anchovy fillets, chopped (optional); 2 tablespoons finely grated lemon zest; 1 tablespoon fresh lemon juice; Kosher salt, freshly ground pepper; Olive oil (for drizzling); Mixed crudité, such as radishes, halved if large, endive, leaves separated, small carrots, scrubbed, trimmed, and/or baby fennel (for serving)