Turn the oven to broil.
In a mini chopper, food processor or blender, blend the feta, yogurt, and pepper until smooth. Depending on your appliance, small quantities may be hard to blend without scraping down the sides many times. You may also work into a smooth paste by hand. A little buttermilk would be an acceptable option to the yogurt.
Place the tomatoes, cut sides up, on a lightly greased baking sheet with sides. Spoon the feta mixture over the tomatoes, trying to keep most of it on the tomatoes. The globs that fall on the sheet will bake to a golden brown and taste delicious, too.
Place in the oven and, watching carefully, broil until the feta topping is golden brown.
Sprinkle with the basil and serve.