In a very small sauté pan, over low-medium heat, warm the Yuzu juice with the lime zest and sugar. Cook just to dissolve the sugar, about 30 seconds. Add the thinly sliced jalapeño and let this come to room temperature while you prepare the fruit.
To prepare the fruit, use a paring knife to cut about 1/2-inch off the top and bottom of the citrus.
Remove the skin by setting the fruit down on one of the flat surfaces and use the knife, moving downwards into the fruit and cutting only slightly into the flesh.
Then cut very thin round slices and cut those in half. (Save the remaining parts of the grapefruits and juice them -- simply to have on hand!)
Arrange the fruit with the basil leaves in a circular pattern on two plates, and drizzle each serving with the Yuzu-Jalapeño sauce.