Preheat the grill or grill pan over medium-high heat.
Brush the ciabatta bread slices lightly with olive oil and season with salt. Set aside.
Combine the halloumi cheese and peach slices in a large bowl. Toss with a drizzle of olive oil– just enough to lightly coat the peaches and cheese. Transfer everything to the grill, in batches if necessary. Grill for 2-3 minutes per side, until grill marks appear. Remove everything from the grill.
Tear apart the grilled ciabatta to create large chunks. Add to a large bowl with the grilled peaches and halloumi. Then combine with the red onion and basil leaves. Set aside.
In a medium-sized bowl, whisk together the remaining olive oil, white balsamic, dijon mustard, honey, salt and pepper. Adjust to taste.
Lightly drizzle the vinaigrette over the panzanella and toss. Transfer to a plate and garnish with additional basil, if desired. Serve with the remaining dressing.