Preheat oven to 400ºF (205ºC). Slide oven racks into the upper and lower third positions. Grease 2 rimmed baking sheets with 2 teaspoons of olive oil on each pan. Alternatively, you can line both baking sheets with parchment paper. You wouldn't need to grease the parchment paper.
If you are using raw or cooked chicken meatballs, set them aside. If you are using raw chicken sausage, chop them into 1-inch chunks. I like digging the ground meat out of the casing and shaping the meat into meatballs.
Chop broccoli browns in to florets. Slice carrots into 1/4-inch thick sticks that are about 3 or 4 inches long. You can also use baby carrots for this. I recommend slicing the thicker carrots in half. Chop potatoes into 1/2-inch chunks.
Toss potatoes with 1 tablespoon of olive oil and a generous pinch of salt. Spread the potatoes over the 2 baking sheets. Slide the baking sheets onto the upper and lower third oven racks and bake potatoes for 20 to 25 minutes.
Toss broccoli florets with 1 tablespoon of olive oil and a pinch of salt. In a separate bowl, toss carrot sticks or baby carrots with 2 teaspoons of olive oil and a pinch of salt.
Remove baking sheets from the oven, and give the potatoes a stir. Spread out the broccoli, carrots and meatballs onto both baking sheets. Bake everything for 15 minutes, until the meatballs are cooked through. The meatballs should register at 165ºF (75ºC). (NOTE: If you are using cooked meatballs, you only need to bake them for 8 to 10 minutes. Add cooked meatballs onto the baking sheet last.)
Remove baking sheets from the oven and season everything with salt and pepper to taste. Brush some sauce on the meatballs, if you like.