Roast, turning vegetables every 10 minutes or so, until they are tender and lightly caramelized, about 15 minutes for broccolini, 25 minutes for carrots and 30 minutes for cauliflower. Meanwhile, in a large bowl, gently and thorughly toss cheese with cornstarch and cayenne. Cornstarch will help thicken your fondue and also prevents the cheese from clumping. Add beer to a medium saucepan and bring to a simmer over medium-high heat, then reduce heat to medium-low. Transfer to a fondue pot and sprinkle with a generous amount of black pepper, keeping it warm over a gentle heat source.