Place basil, jalapeno, ¼ cup of olive oil, water, and salt in a food processor and puree until smooth. Scraping down the container as needed. Place the sauce aside.
Preheat a grill or grill pan to high.
Brush the peaches (cut side) with olive oil. Grill 3-4 minutes on each side, or until caramelized with grill marks and softened. Once cool enough to handle, slice each half into wedges. Arrange the peach wedges on a platter, or individual plates.
Brush both sized of the halloumi with olive oil. Grill 2-3 minutes on each side, or until the cheese starts to soften (just before it melts) and develops grill marks.
Place the grilled halloumi slices on the platter or plates with the peaches. Spoon the basil jalapeno sauce on top of the peaches and halloumi. Serve immediately with grilled bread and wine.