Add the cauliflower florets to a large bowl. Drizzle with olive oil, season with salt and toss. Transfer to a baking sheet and roast until the cauliflower is very brown and crispy, about 30 minutes. Remove from the oven to a large bowl and reserve.
Coat a large saute pan generously with olive oil. The oil should be about 1/8-inch deep. Heat the pan over medium-high heat. When the oil is hot, add the capers. As the capers cook they will open up and start to look like little flowers (very cute). Fry the capers until they are crispy, about 3 to 4 minutes. Remove the capers from the pan, dry them on paper towels and season with salt immediately.
Toss together the cauliflower, capers, radicchio, pecorino, and chives. Dress the salad with lemon juice, olive oil and salt, to taste. Divide between 4 serving plates or arrange on 1 big platter and serve.