Put the onions in a bowl of water and put them in the fridge. Heat the oven to 300. Spread the bread out on a cookie sheet and toast it in the oven until just barely toasty - maybe 7-10 minutes.
Put the oil, vinegar, cider, honey, shallots, salt and pepper in the blender and whiz.
Put the bread in a large mixing bowl. Cut the apple in to wedges and then cut those in half, into the bowl along with the onions (which you have drained and patted dry). Add the dressing and toss it together. Grate or shave the cheese and toss again. Add the arrugula and basil and toss again. Taste a leaf and decide if you want more pepper.