I had eaten at MBB downtown once and was a fan of the food they served there. I really am behind the city's initiative to encourage local successful restaurants to open up locations in Sky Harbor airport, and Matt's Big Breakfast is a treat! They also have Lolo's Chicken n' Waffles, Deluxe Burger and Chelsea's Open Kitchen to name a few local fav spots that we frequent in town and at PHX.
MBB is precisely what it sounds like Big Breakfasts. Keep in mind, it is located at Terminal 4 AFTER YOU CLEAR SECURITY. Whatever tickles your first meal of the day fancy can be tickled deeply and thoroughly here. The menu is a true journey through morning comfort food presented in more bountiful and gourmet style that your regular combo #6 at your local slop n' drop diner. Last time I ate there before a flight I had a massive omelette with rosemary potatoes (which are amazing btw). My wife had poached eggs and off the bone ham which seemed to have come right from the farm!
The only caution I would give is to make sure you have time to have a sit-down-and-order mea. The service is pretty fast but the clients come in waves and everyone seems to need to catch the same flight. l had to chase down our server to run my card as it seemed everyone in the place was trying to pay at once and were likely mostly on the same flight so be sure you're not in a photo-finish situation to your gate.
For those in a rush, I think they also have a walk-up counter and sling breakfast sammies to go for those wanting to stink up economy class with their brought-on food...a practice I abhor. I never bring hot food onto a plane. It's rude. Bring a cold sandwich or a salad and leave your stinky McRaunchy's or Blazing burritos in the terminal!
MBB...come hungry and then enjoy your post breakfast drooling coma as you soar the clear blue skies!