Friar's Nook (Fantasyland) has breakfast sandwiches and tots as well as little do-nut bites. The sandwiches are not 5-star, but a solid "good" and the tots are really good (if that makes sense). They open at the same time as official park opening and have Mobile order so you don't have to stand in a long line like Starbucks.
Sleepy Hollow has waffles (I can't remember if they have Mobile Order)
The Lunching Pad (Tomorrow Land) has breakfast sandwiches (most likely the same ones that Friar's Nook has!), the Cheshire Cat Tail (super sweet), and you can get a hot dog in the morning, too. They DO have Mobile Order, too. Though it isn't listed on the menu online, I think we were able to order a Mickey Pretzel with Cheese in the morning, too.
I am very much a "I need protein" in the morning person, so right before my last trip, I did a practice Mobile Order for MK to see what was available ;-)
PS - edited to add- Gaston's Tavern opens with the park, too, but they only have that Cinnamon Role and a cupcake in the mornings...and I noticed the line was SUPER LONG as in May they weren't using Mobile Order.