Prep the vegetables
Preheat oven to 400ºF (200ºC). Toss the broccoli, cauliflower and carrots in the olive oil and arrange in a single layer on an aluminum-foil-lined baking sheet.
Roast the vegetables
Season with salt and pepper and roast until tender and lightly browned, about 20 to 25 minutes.
Heat a medium saucepan over medium heat, add the butter and allow to melt. Add the garlic and shallots and cook, stirring occasionally until the shallots are soft, about 4 minutes.
Add the beer and Worcestershire and bring to a simmer.
Toss cheese in cornstarch
In a small bowl toss the shredded cheese with the cornstarch, chili powder, paprika and cayenne.
Add the cheese
Add the cheese mixture slowly, stirring constantly until all the cheese has melted.
Garnish with chives and serve hot with the roasted vegetables and soft pretzels on the side.