Grill-Roasted Vegetables with Pine Nut Pesto

carrots, cut into 1-inch pieces

parsnips, cut into 1-inch pieces

brussels sprouts, halved lengthwise

butternut squash—peeled, seeded and cut into 1/2-by-1 1/2-inch pieces

large shallots, cut into 1/2-inch wedges

thyme sprigs

extra-virgin olive oil

Salt and freshly ground pepper

plus 2 tablespoons pine nuts

unsalted butter

large garlic clove, thinly sliced

freshly grated Parmigiano-Reggiano cheese