Toss the broccoli florets with 2 teaspoons oil and some salt and pepper in a small bowl. Divide a nonstick half-sheet pan (13-by-18-inches) into four quadrants and place the broccoli in one quadrant in a single layer. Repeat with the carrots, bell pepper and onion, tossing each with 2 teaspoons oil and some salt and pepper and spreading in a single layer in its own quadrant. Roast until the vegetables are softened slightly and deeply browned, 15 to 18 minutes. Remove the sheet pan and lower the oven to 350 degrees F.
Meanwhile, whisk together the eggs and cream in a large bowl and sprinkle with some salt and pepper. Drizzle the remaining tablespoon oil over the top of the vegetables, then pour the egg mixture over the top. Sprinkle the cheese evenly over the eggs. Bake, rotating once halfway through, until the eggs are completely cooked through, puffed and just the slightest bit golden, 12 to 15 minutes.
Slice the frittata into portions and use an offset spatula to remove from the pan. Sprinkle with chives and serve.