Preheat oven to 425℉. Grease a large baking dish (9-by-13 inch) with a teaspoon of oil (or use oil spray if you prefer).
Place diced sweet potato in the baking dish. Drizzle with a teaspoon of oil and sprinkle with a pinch of salt and a few grinds of black pepper. Toss to coat then spread into an even layer. Roast until the potato starts to soften and brown, about 15 minutes.
Toss the broccoli and peppers with the remaining teaspoon of oil and season with salt and pepper. Scatter the broccoli and peppers over the partially cooked sweet potato then continue to roast. Cook until the broccoli tops begin to brown, about 10 minutes.
Meanwhile, in a large bowl, whisk together the eggs, milk, and pesto. Season with a pinch of salt and a few grinds of black pepper. Cut tomatoes crosswise into 4 to 5 slices and set aside.
Once vegetables are browned, remove the pan from the oven. Reduce the oven temperature to 350℉.
Whisk the egg mixture again to make sure everything is well combined then pour it over the vegetables. Place sliced tomatoes over the top of pan in rows then scatter with half of the chives or green onions.
Bake until cooked through and the center of the casserole is firm, 20 to 25 minutes.
Allow to cool for 5 to 10 minutes, sprinkle with remaining chives/green onions, then slice into squares. Serve warm or at room temperature. Store leftovers in fridge for up to 4 days.