Pre-heat the oven to 325 degrees.  In an iron skillet pan, heat the oil on medium high heat.  Add the onions and begin to soften.  About 2 -3 minutes in, add the peppers and cook for 2 – 3 more minutes.
To finish the vegetables, add the broccoli and cook for another 2 minutes.
Beat the eggs in a bowl together with the milk.  Beat until they are fluffy.  This will take 1 – 2 minutes.  Transfer the vegetables to a fritatta pan.  Add the eggs and let set a little before stirring.
Let them set a couple more times.  You do not want them to cook fully but to begin to firm up.  Add the cheddar cheese and mix.  Remove from the stove top and place in the oven.  After cooking for about 5 minutes, top with the rest of the cheese.
Finish cooking for 2 – 3 more minutes.