TexasSweet.com with a few little changes. Other addition suggestions: orange blossom water, cardamom, rosewater, cracked black pepper, crystallized ginger, ground cloves, etc. I love grapefruit-it is in fact my favorite fruit. If you are still concerned about the tartness you can replace up to a third of the grapefruit with fresh orange segments.
Cut the grapefruit in half. Peel and remove seeds and pith. Cut into chunks. Place the grapefruit chunks individually on a sheet pan or similar. Cover with plastic wrap and freeze for about 45 minutes or until slightly frozen.
Place the partially frozen grapefruit sections in a food processor along with the Greek yogurt, sugar and vanilla extract. Process for 1 minute or until smooth and creamy. Taste the mixture and if you think it needs more sugar add some.
Transfer to a freezer container and freeze until firm. Once firm, scoop into individual serving dishes. Garnish with fresh mint.