Lemony Pasta with Cauliflower, Chickpeas, and Arugula

extra-virgin olive oil, divided

drained capers, patted dry

small or 1/2 large head of cauliflower (about 1 pound), cut into small florets

garlic cloves, finely chopped

kosher salt, plus more

freshly ground black pepper

chickpeas, drained, rinsed, patted dry

cold unsalted butter, divided

casarecce, gemelli, or other medium pasta

fresh lemon juice

baby arugula