How to Make It
In a medium bowl, whisk both of the flours with the salt. In a large bowl, whisk the water with the yeast until the yeast dissolves. Whisk in 1 tablespoon of the olive oil. Add the flours and stir with a wooden spoon until a dough forms. Turn out onto a lightly floured work surface and knead until smooth, about 10 minutes. Transfer the dough to a lightly oiled bowl and press a sheet of plastic wrap directly on the surface. Refrigerate overnight.
Line a baking sheet with parchment paper. Cut the dough in half and form each piece into a ball; set them about 3 inches apart on the prepared sheet and cover with plastic wrap. Let stand at room temperature until doubled in bulk, 3 hours.
Light a grill. On a lightly floured work surface, using a lightly floured rolling pin, roll out each piece of dough into a 10-inch round and brush the tops with 2 tablespoons of the olive oil. Oil the grate and grill the dough oiled side down over moderate heat until lightly charred, 2 to 3 minutes. Brush the tops with the remaining 2 tablespoons of olive oil and flip. Arrange the peaches, cheddar cheese and red onion on top, cover and grill until the cheese is melted and the pizzas are lightly charred on the bottom, 2 to 3 minutes more. Transfer to a work surface. Garnish with parsley and chives, slice and serve immediately.