Preheat the oven to 400F. Trim the cauliflower and cut it into florets. Arrange on a large baking sheet. Toss with olive oil and salt. Roast for 25-30 minutes, or until golden.
While the cauliflower is roasting, you can use the lower oven rack to toast the breadcrumbs and the walnuts. Toast the walnuts around 5-7 minutes until fragrant but not dark. When cool, roughly chop.
To make the breadcrumbs, tear the stale bread. Then add it to a food processor and pulse into chunky crumbs. Transfer to baking tray add the grated garlic, grated lemon zest, olive oil, and a big pinch of salt. Massage everything together with your hands to make sure the crumbs are evenly coated. Spread on the tray and bake for 10 minutes, or until golden. Combine with the walnuts and set aside. Wait to add them to the salad just before serving so they stay crunchy. If you are bringing this dish to a picnic or potluck, store the breadcrumb-walnut mixture separately and add at the last minute.
Make the vinaigrette in the big salad bowl you will use for serving. Rinse and chop the capers. Add them to the bottom of the salad bowl along with the grated garlic, salt, and champagne vinegar or lemon juice. Add the olive oil in a steady stream and whisk vigorously to get a thick, creamy dressing. Taste and adjust the seasoning if desired.
To serve, add the cauliflower and parsley to the vinaigrette. Just before serving, add the breadcrumbs and walnuts. Toss and taste for salt.
If you have leftovers, I recommend reheating in a toaster oven so the breadcrumbs get crispy again.