Using a sharp knife cut the ends off of a large grapefruit.
Set it onto a cutting board with one of the flat sides down. And carefully use a sharp knife to remove the skin and white pith from the grapefruit.
Once the grapefruit is cleaned, working over a small bowl, use the sharp knife to make cuts next to the white lines on the fruit. Cut on each side and remove the grapefruit segment and place it into the bowl below.
Once you have freed all of the grapefruit segments, squeeze the remaining fruit releasing the grapefruit juice onto the segments in the bowl.
Add the shallots, fresh chopped mint leaves, white wine vinegar, and sugar to the bowl containing the grapefruit segments and juice.
Add the extra virgin olive oil and using a wire whisk, combine the ingredients breaking apart the segments of grapefruit a little bit.
Serve the vinaigrette on your favorite leafy greens or fish and chicken.